Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500

Question

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

Answer 1

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
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We can simplify these.  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
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-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

Answer 2

Graph and locate turning points.

500B + 300M ≤ 75000

100B + 90M  ≤ 18000

 

P = 300B + 150M