E Pharmed Caplets is an antibiotic product with monthly sale

E. Pharmed Caplets is an antibiotic product with monthly sales revenues and costs as described below: TR = 9000-0100° TC 43,000 +2000 +0.4002 Q16. Derive the MR function. Q17. Derive the MC function. Q18. Calculate the output level that will maximize profit. Q19. Calculate total revenue. 020. Calculate total cost. Q21. Calculate this maximum profit.

Solution

16.

MR = d(TR)/dQ = 900-2*.1Q

MR = 900-.2Q

17.

MC = d(TC)/dQ = 200 + 2*.4*Q

MC = 200+.8Q

18.

To maximize the output level,

MR = MC

900-.2Q = 200+.8Q

Q = (900-200)/1

Q = 700 units

19.

Total revenue = 900*700 - .1*700^2 = $581000

20.

Total cost = 43000 + 200*700 +.4*700^2 = $379000

21.

Maximum profit = total revenue – total cost = 581000 – 379000

Maximum profit = $202000