Question

1. The total cost to manufacture and sell q cars is given by the cost equation C(q)=2000+59 The revenue equation is R(q)= 40q-0.050 dollars for the sale of q exactotherms. Assume the profit is P(q) = R(q) - C(q). a. Find the marginal cost. b. Find the marginal revenue. c. What is the profit equation? P(q) = 2. a. Find the number of items q to sell so that the profit function P(q) has its maximum Confirm that you answer to a is correct by doing the next two parts. b. Find on which interval(s) the profit function is increasing. c. Find on which interval(s) the profit function is decreasing. Test the first derivative to answer parts b and C. Do your work for parts b and c below d. Use you work in parts b and c to justify that your answer to a is correct

Answer 1

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0 Cost function C(q) = 2000 159 Revenue function R(q) = 409-0.05q² la @ marginal cost = mccas= c'ca) La (2000+59) 0+ 50 Meq) = 5 marginal Revenue MR (9) = Rica) (409-00059²) MALO) = 40- od 28.05(29) Mala) = 40-0.109 S © profit equation pca)= R(q)-ccq) pea)= (4.09.-0-0523)-2000 4kv) P(q) = 359 -0.059²-2000