Jessica owns a company that makes pre-packaged sandwiches for convenience stores.The market price for a sandwich is $5 and Jessica is a price-taker.Her daily cost for making sandwiches is C(Q)= 2.5Q + (Q²/40)and her marginal cost is MC = 2.5 + (Q/20).What should Jessica do if she has an unavoidable fixed cost of $150 a day? A) She should keep producing sandwiches because she has a positive sales quantity B) She should keep producing sandwiches because she is maximizing profit at the current quantity C) She should shut down production because his profit less the unavoidable cost is negative D) She should shut down production because his profit less the unavoidable cost is positive

Question

Quizplus · Accepted Answer

To determine whether Jessica should continue to produce sandwiches, we need to calculate her profit. Using the given information, profit can be calculated as follows:
Profit = (Price - Marginal Cost) * Quantity - Fixed Cost
Profit = ($5 - (2.5 + Q/20)) * Q - $150
Simplifying this equation:
Profit = $(2.5Q - 0.05Q^2 - 150)
To maximize profit, we need to find the quantity that maximizes this profit function. The maximum profit occurs where the derivative of the profit function equals zero. Taking the derivative of the profit function with respect to Q:
dProfit/dQ = 2.5 - 0.1Q
Setting this equal to zero and solving for Q:
2.5 - 0.1Q = 0
Q = 25
At a quantity of 25, profit is:
Profit = $(2.5*25 - 0.05*25^2 - 150) = $-42.5
Since profit is negative, Jessica should shut down production.

Jessica Owns a Company That Makes Pre-Packaged Sandwiches for Convenience