Question

For Insomnia Cookies, the total cost of producing cookies, k and frosting, f, jointly is given by

TC = 100 + 50kf – (kf)^0.5.

The total cost of producing k and f in two different factory locations is given by

TC = 75 + 3,000k + 1,000Q₂ + k² + f². (Q stands for quantity)

If the firm produces k = 40 and f = 100, then how much more expensive or cheaper in percentage terms is it to produce together? If it's more expensive, put a negative sign in front of your answer. You may answer either as a decimal or a typical percentage (rounded to two decimal places in either case).

Answer 1

K = 40 and F =100. So, Q = 140 (100+40)

Case 1: K and F produced together

When K and F are produced together TC = 100 + 50kf – (kf)^0.5.

Given K and F: TC = 100 + 50*100*40 – (100*40)^0.5.

TC = 200036.76

Case 2: K and F produced separately

When K and F are produced separately TC = 75 + 3,000k + 1,000Q₂ + k² + f².

Given K, F and Q: TC = 75 + 3000*40 + 1000*140 + (40*40) + (100*100)

TC = 271675

Clearly, TC in case 2 is more than TC in case 1

Therefore, it means that it is cheaper to produce the items together.

Now to calculate the percentage we divide the difference between the two TC by TC in case 1

So the required percentage =( (TC1 - TC2 )/ TC1 )* 100

= (( 271675 - 200036.76 )/ 200036.76 )* 100

~ 35.81 %

So, it is approximately 34% cheaper to make products together as compared to making them separately.

If this answer has been useful then please give an upvote.