Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelv

Question

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function?

Max Z = 75B + 85M

Max Z = 85B + 75M

100B + 50M ? 25000

100B + 50M ? 25000

100B + 80M ? 18000

100B + 80M ? 18000

Explanation / Answer

he company has only $25000 to invest so the total cost they can afford is $25000

cost for big shelves is 100B where B is number of Big shelves and 100 is cost of each big shelve

similarly cost for medium shelves is M*50 where M is number of medium shelves and 50 is cost of each medium shelve

now total cost is = 100B+50M <= total investment they can afford

So, 100B+50M < = 25000

similarly for the space

space for big = 100*B where here 100 is space for each big shelve

space for medium = 80*M where here 80 is space for each medium shelve

total space is = 100*B+80*M <= total space they can provide

100*B+80*M <= 18000

similarly profit= maxZ= profit for BIG+ profit for Medium

=85B+75M

maxZ = 85B+75M

so option B and C and E are correct

Option E is 100*B+80*M <= 18000

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