question archive 1)LIKNA Furniture buys two products for resale: Book shelves (B)and Cloth shelves (C)
1)LIKNA Furniture buys two products for resale: Book shelves (B)and Cloth shelves (C)
Subject:AccountingPrice:2.84 Bought3
1)LIKNA Furniture buys two products for resale: Book shelves (B)and Cloth shelves (C). Each book shelf costs $500 and requires 100 cubic feet of storage space, and each cloth shelf costs $300 and requires 90 cubic feet of storage space. The company has cost budget $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each book shelf is $300 and for each cloth shelf is $150.
- Formulate the Linear Programming Model and solve by mathematical solution
- Determine the sensitivity range for profit for Medium Shelf
- Determine the sensitivity range for cost
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Taking the equations Mark M set up,
let's completely fill the storage space 18,000 ft3
and spend the entire $75,000
equation 1: 500B + 300M = 75000
equation 2: 100B + 90M = 18000
-----------------------------
simplifing equation
Divide equation 1 by 100
and divide equation 2 by 10
equation 1: 5B + 3M = 750
equation 2: 10B + 9M = 1800
multiply equation 1 by -3 and add the equations
15B - 9M = -2250
10B + 9M = 1800
-----------------------
-5B = -450
B = 90
Substitute 90 in place of B in equation 2
10(90) + 9M = 1800
900 + 9M = 1800
9M = 900
M = 100
If we purchase 90 big shelfs and 100 medium shelfs
we fill the entire storage space and spend the $75,000
P = 300B + 150M
P = 300(90) + 150(100)
P = 27,000 + 15,000
P = 42,000
Profit = $42,000
