Problem 9-11 Edwards Manufacturing Company purchases two component parts from three different suppliers

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Problem 9-11 Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Supplier 1 Component 1 fill in the blank 1 2 3 fill in the blank 2 fill in the blank 3 Component 2 fill in the blank 4 fill in the blank 5 What is the total purchase cost for the components? fill in the blank 6 $ fill in the blank 7 Problem 9-13 (Algorithmic) Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an asneeded basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.48 per pound for Brazilian Natural and $0.61 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend Bean Regular DeCaf Brazilian Natural 80% 40% Colombian Mild 20% 60% Romans sells the Regular blend for $2.8 per pound and the DeCaf blend for $4.4 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 850 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.75 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.14 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. Let BR = pounds of Brazilian beans purchased to produce Regular BD = pounds of Brazilian beans purchased to produce DeCaf CR = pounds of Colombian beans purchased to produce Regular CD = pounds of Colombian beans purchased to produce DeCaf If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if Max fill in the blank 1 BR + fill in the blank 2 + BD fill in the blank 3 CR + fill in the blank 4 CD s.t. fill in the blank 5 + BR fill in the blank 6 = CR fill in the blank 8 + BD fill in the blank 11 fill in the blank 9 CD fill in the blank 12 BR = CR fill in the blank 14 + BD = fill in the blank 15 CD = fill in the blank 7 fill in the blank 10 fill in the blank 13 fill in the blank 16 BR, BD, CR, CD ≥ 0 there is a + sign before the blank. (Example: -300) The complete linear program is What is the contribution to profit? Optimal solution: BR = fill in the blank 17 BD = fill in the blank 18 CR = fill in the blank 19 CD = fill in the blank 20 If required, round your answer to two decimal places. Value of the optimal solution = $ fill in the blank 21 Problem 9-01 The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. a. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? Let T = number of television spot advertisements R = number of radio advertisements N = number of newspaper advertisements Budget $ T = fill in the blank 1 4 fill in the blank 2 8000 R = fill in the blank 3 N = fill in the blank 5 14 10 fill in the blank 4 fill in the blank 6 4200 6000 18200 b. What is the total audience reached? fill in the blank 7 c. 1052000 By how much would audience contact increase if an extra $100 were allocated to the promotional budget? fill in the blank 8 5130 Problem 9-07 (Algorithmic) As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year 1 2 3 4 5 6 Payment 170 210 250 310 340 500 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 3.25% annually) and government securities, at prices and rates currently quoted in The Wall Street Journal. Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value = $1000). Funds not invested in these securities will be placed in savings. Security Current Price Rate (%) Years to Maturity 1 $1075 6.55 3 2 $1000 5.125 4 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan. a. Use linear programming to find the minimum cash settlement necessary to fund the annual payments. Let F = total funds required to meet the six years of payments G1 = units of government security 1 G2 = units of government security 2 Si = investment in savings at the beginning of year i Note: All decision variables are expressed in thousands of dollars. If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Min F s.t. fill in the blank 1 F fill in the blank 6 G1 fill in the blank 11 G1 + + + fill in the blank 2 G1 fill in the blank 7 G2 fill in the blank 12 G2 + + + fill in the blank 3 G2 fill in the blank 8 S1 fill in the blank 13 S2 + + + fill in the blank 4 S1 fill in the blank 9 S2 fill in the blank 14 S3 = = = fill in the blank 5 fill in the blank 10 fill in the blank 15 fill in the blank 16 G1 + fill in the blank 17 G2 fill in the blank 21 G2 + + fill in the blank 18 S3 fill in the blank 22 S4 fill in the blank 25 S5 + + + fill in the blank 19 S4 fill in the blank 23 S5 fill in the blank 26 S6 = = = fill in the blank 20 fill in the blank 24 fill in the blank 27 Round your answer to the nearest dollar. If an amount is zero, enter "0". Current investment required $ fill in the blank 28 Investment in government security 1 $ fill in the blank 29 Investment in government security 2 $ fill in the blank 30 Investment in savings for year 1 $ fill in the blank 31 Investment in savings for year 2 $ fill in the blank 32 Investment in savings for year 3 $ fill in the blank 33 Investment in savings for year 4 $ fill in the blank 34 Investment in savings for year 5 $ fill in the blank 35 Investment in savings for year 6 $ fill in the blank 36 b. Use the dual value to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000. Round your answer to the nearest dollar. $ fill in the blank 37 c. Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000. Round your answer to the nearest dollar. Hoxworth should be willing to pay anything less than $ fill in the blank 38 d. . Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Note: All decision variables are expressed in thousands of dollars. If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Min F s.t. 1) 2) fill in the blank 39 F fill in the blank 44 G1 + + fill in the blank 40 G1 fill in the blank 45 G2 + + fill in the blank 41 G2 fill in the blank 46 S1 + + fill in the blank 42 S1 fill in the blank 47 S2 = = fill in the blank 43 fill in the blank 48 3) 4) fill in the blank 49 G1 fill in the blank 54 G1 + + fill in the blank 50 G2 fill in the blank 55 G2 fill in the blank 59 5) G2 + + + fill in the blank 51 S2 fill in the blank 56 S3 fill in the blank 60 S4 fill in the blank 63 6) S5 fill in the blank 66 7) S6 + + + + + fill in the blank 52 S3 fill in the blank 57 S4 fill in the blank 61 S5 fill in the blank 64 S6 fill in the blank 67 S7 = = = = = fill in the blank 53 fill in the blank 58 fill in the blank 62 fill in the blank 65 fill in the blank 68 How much would Hoxworth save if this change could be negotiated? Round your answer to the nearest dollar. $ fill in the blank 69 200Problem 9-05 (Algorithmic) Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.4, on one serving of Dial 911, $0.53. Each serving of Wimpy requires 0.2 pound of beef, 0.2 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.2 pound of beef, 0.35 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 15 pounds of beef, 10 cups of onions, 84 ounces of Kilgore’s special sauce, and 55 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let W = number of servings of Wimpy to make D = number of servings of Dial 911 to make Max fill in the blank 1 W + fill in the blank 2 D s.t. fill in the blank 3 W + fill in the blank 4 D fill in the blank 7 W + fill in the blank 8 D fill in the blank 11 W + fill in the blank 12 D fill in the blank 15 W + fill in the blank 16 D W, D b. fill in the blank 6 fill in the blank 10 fill in the blank 14 fill in the blank 18 ≥0 Find an optimal solution. If required, round your answers to two decimal places. W = fill in the blank 19 , D = fill in the blank 20 , Profit = $ fill in the blank 21 (Beef) (Onions) (Special Sauce) (Hot Sauce) c. What is the shadow price for special sauce? If required, round your answers to two decimal places. $ fill in the blank 22 Interpret the shadow price. The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. Increase the amount of special sauce available by 1 ounce and re-solve. If required, round your answers to two decimal places. W = fill in the blank 24 , D = fill in the blank 25 , Profit = $ fill in the blank 26 Does the solution confirm the answer to part (c)? Yes, as the shadow price is confirmed / No as the shadow price not confirmed Problem 9-15 Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming two-week period are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown. Develop and solve a linear programming model to maximize contribution to profit. Let Ri = the number of barrels of input i to use to produce Regular, i=1,2,3 Si = the number of barrels of input i to use to produce Super, i=1,2,3 If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) fill in the fill in the fill in the fill in the fill in the fill in the blank 1 blank 2 blank 3 blank 4 blank 5 Max + + + + + blank 6 100 s.t. R1 87 R2 110 R3 100 S1 87 S2 110 S3 fill in the blank 7 100 fill in the + blank 8 100 R1 fill in the blank 10 87 fill in the ≤ blank 9 110000 S1 fill in the + blank 11 + 87 R2 fill in the blank 16 100 R1 fill in the + blank 18 87 110 R2 fill in the + blank 14 110 R3 fill in the + blank 17 R1 fill in the blank 30 100 S1 fill in the + blank 21 fill in the + blank 22 87 110 S2 S3 fill in the + blank 25 fill in the + blank 26 fill in the ≥ blank 27 fill in the + blank 28 fill in the + blank 29 87 110 100 87 110 R2 R3 R1 R2 fill in the + blank 32 fill in the ≥ blank 33 fill in the + blank 34 fill in the + blank 35 87 110 100 87 110 S2 S3 S1 S2 fill in the ≤ blank 23 500000 R3 fill in the + blank 31 S1 R1, R2, R3, S1, S2, S3 ≥ 0 300000 350000 R3 100 100 S3 fill in the ≤ blank 15 fill in the ≤ blank 19 fill in the blank 20 fill in the blank 24 350000 S2 fill in the blank 13 110 fill in the ≤ blank 12 S3 What is the optimal contribution to profit? Maximum Profit = $ fill in the blank 36 blank 38 500000 2845000 by making fill in the blank 37 260000 barrels of Regular and fill in the barrels of Super. Problem 9-17 Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows: a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased? If required, round your answers to one decimal place. Let FM = number of frames manufactured FP = number of frames purchased SM = number of supports manufactured SP = number of supports purchased TM = number of straps manufactured TP = number of straps purchased fill in the Min blank 1 fill in the + blank 2 FM fill in the + blank 3 FP fill in the + blank 4 SM fill in the + blank 5 SP TM fill in the + blank 6 TP s.t. fill in the + blank 7 3.5FM fill in the + blank 8 SM fill in the blank 10 fill in the ≤ blank 9 TM fill in the ≤ blank 11 + 1.7SM FM fill in the blank 12 fill in the + blank 13 FM fill in the ≤ blank 14 + 1.7TM SM fill in the + blank 15 FM fill in the ≥ blank 16 FP SM fill in the + blank 17 fill in the ≥ blank 18 SP TM fill in the + blank 19 fill in the ≥ blank 20 TP FM, FP, SM, SP, TM, TP ≥ 0. Manufacture Frames fill in the blank 21 fill in the blank 22 Supports fill in the blank 23 fill in the blank 24 Straps b. Purchase fill in the blank 25 fill in the blank 26 What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar. $ fill in the blank 27 c. How many hours of production time are used in each department? Hours of production time used Department d. Cutting fill in the blank 28 hours Milling fill in the blank 29 hours Shaping fill in the blank 30 hours How much should Frandec be willing to pay for an additional hour of time in the shaping department? $ fill in the blank 31 e. Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity? Yes or No Why or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Problem 9-09 (Algorithmic) Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system problems and for the rebooking of flights for customers whose plans have changed or whose travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon’s management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers. Epsilon analysts have estimated the minimum number of call center employees needed by day of the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows: Minimum Number of Day Employees Needed Monday 90 Tuesday 45 Wednesday 60 Thursday 50 Friday 90 Saturday 70 Sunday 45 The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week. Each call center employee receives the same salary. Assume that the schedule cycles and ignore start up and stopping of the schedule. Develop a model that will minimize the total number of call center employees needed to meet the minimum requirements. Let Xi = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday...) Min X1 + X2 + X3 + X4 + X5 + X6 + X7 s.t. X1 + X4+ X5+ X6+ X7 =, ≥, ???????? ≤ X5+ X6+ X7 =, ≥, ???????? ≤ X6+ X7 =, ≥, ???????? ≤ X7 =, ≥, ???????? ≤ X1 + X2+ X1 + X2+ X3+ X1 + X2+ X3+ X4+ =, ≥, ???????? ≤ X1 + X2+ X3+ X4+ X5 =, ≥, ???????? ≤ X2 + X3+ X4+ X5+ X6 X3 + X4+ X5+ X6+ X7 X1, X2, X3, X4, X5, X6, =, ≥, ???????? ≤ X7 ≥ fill in the blank 2 fill in the blank 4 fill in the blank 6 fill in the blank 8 fill in the blank 10 fill in the blank 12 fill in the blank 14 0 Find the optimal solution. X1 = fill in the blank 15 X2 = fill in the blank 16 X3 = fill in the blank 17 X4 = fill in the blank 18 X5 = fill in the blank 19 X6 = fill in the blank 20 X7 = fill in the blank 21 Total Number of Employees = fill in the blank 22 Give the number of call center employees that exceed the minimum required. Excess employees: Monday = fill in the blank 23 Tuesday = fill in the blank 24 Wednesday = fill in the blank 25 Thursday = fill in the blank 26 Friday = fill in the blank 27 Saturday = fill in the blank 28 Sunday = fill in the blank 29