Question

There is a firm making custom stuffed animals. The demand function for custom stuffed animals is: P = 1000 - 20Q

The cost depends on how much of each of their inputs they use. It takes 3 inputs to make a stuffed animal: cotton, oil, and chorizo. The amount required, input prices, and restrictions are below:

It takes 1 pound of cotton to make a stuffed animal. Cotton costs $20 per pound. They can buy up to 23 pounds of cotton.

It takes 2 barrels of oil to make a stuffed animal. Oil costs $10 per barrel. They can buy up to 44 barrels of oil.

It takes 3 chorizo burritos to make a stuffed animal. Burritos cost $5 per burrito. They can buy up to 100 burritos.

Set this up in Solver to help them maximize profit by choosing the best quantity of stuffed animals to produce, subject to the constraints of the maximum amount of cotton/oil/burritos they can buy. What is the profit that the firm will earn when they maximize their profit?

Answer 1

Ans. As they need 1 pound of cotton, 2 barrels of oil, 3 burritos, thus max quantity they can produce is 22 animals.

At 22 qty, P= 1000-22*20

P= 560

Revenue = 560*22 = 12320

Cost = 22*20 + 22*2*10 + 22*3*5 ( cotton+ oil + burritos)

= 440+440+330

= 1210

Profit = 11110

At 21 Qty

P= 580

Revenue= 21*580 = 12180

Cost = 21*20 + 21*2*10 + 21*3*5

=420+420+315

=1155

Profit= 11025

As profit is decreasing with decrease in quantity and max quantity is 22 therefore best quantity of stuffed animals to produce is 22 and profit thereon is 11110.