Help Much Appreciated

Question

Judy runs a small business with crafted handmade products selling for $350 per product. The producing cost is fixed at $3550 monthly and the variable cost is $(5.5q - 120) per product, where q is the quantity of products produced per month.

a. Find Judy’s minimum total cost & corresponding level of production.

b. Judy claims that as long as she sells 50 products per month she will break even.

c. What is Judy’s maximum monthly profit & corresponding level of production.

Answer 1

a. Find Judy’s minimum total cost & corresponding level of production.

We assume she cant have negative production.

Her variable cost function is linearly increasing. That means it will be at the minimum when production q=0. This also makes logical sense as if she produces nothing she has the least associated variable costs possible.

C_min = 3550 + (5.5*0 - 120) = 3550 - 120 = $3430

However, as a sanity check, it does not make sense for the variable cost function to have a negative, so there may be a problem in how the question is written.

b. Judy claims that as long as she sells 50 products per month she will break even.

P = 350*q

C = 3550 + (5.5*q - 120)

She breaks even when P = C

P(50) = 350*50 = 17500

C(50) = 3550 + (5.5*50 - 120) = 3705

P > C so she will be beyond breaking even. However, q = 50 is not the break even quantity

c. What is Judy’s maximum monthly profit & corresponding level of production.

There are no production constraints in the problem and the cost function is linear. Since her sale price is always more than the variable cost, her profit will increase as long as quantity does. Therefore P_max at q = infinity