question archive Tommy & Lefebvre is Ottawa's full-line authorized dealer for Atomic snowboards for the 2020-2021 winter season
Tommy & Lefebvre is Ottawa's full-line authorized dealer for Atomic snowboards for the 2020-2021 winter season
Subject:Operations ManagementPrice:2.87 Bought7
Tommy & Lefebvre is Ottawa's full-line authorized dealer for Atomic snowboards for the 2020-2021 winter season. T&L's sales projections for November, December and January are 550, 800, and 300 snowboards for each of these next three months. Atomic has agreed to provide T&L with up to 650 boards each month at a unit cost of $82. Using "rush orders", Atomic can also provide T&L with up to 50 additional boards per month at an increased unit cost of $97 each. Boards not sold at the end of the month in which they are in stock are stored in the T&L store at a cost of $20 per board per month. It takes the store clerks 0.5 hours per board to set up, sticker, and display the snowboards and clerk capacity is limited to 500, 600, and 400 hours in each of the 3 months respectively. Finally, T&L have 50 Atomic snowboards from last season (2020 model) that they can sell this year and they want to have at least another 75 snowboards (2021 model) left at the end of January.
Write down the algebraic/mathematical formulation of this problem as a linear programming problem to minimize the total cost to T&L of purchasing and stocking the snowboards. (Define the decision variables, objective function, and constraints).
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Answer:
Decision variables:
Let
Xi = number of snowboards procured using normal orders
Yi = number of snowboards procured using rush orders
Wi = number of snowboards, stored in T&L store
Objective functions:
Min Z = 82X1 + 82X2 + 82X3 + 97Y1 + 97Y2 + 97Y3 + 20W1 + 20W2 + 20W3
Subject to constraints:
X1 + Y1 - W1 = 500 (sales projections of November = 550 - 50 = 500) due to T&L have 50 Atomic snowboards from last season
X2 + Y2 - W2 + W1 = 800 (sales projections of December = 800)
X3 + Y3 - W3 + W2 = 300 (sales projections of January = 300)
0.5X1 <= 500 (limited clerk capacity in November)
0.5X2 <= 600 (limited clerk capacity in December)
0.5X3 <= 400 (limited clerk capacity in January)
W3 >= 75 (at least 75 snowboards required at the end of January)
X1, X2, X3 <= 650 (maximum production using regular time)
Y1, Y2, Y3 <= 50 (maximum production using rush orders)
Xi, Yi, Wi >= 0 (non negativity constraints) ; i = 1,2,3
