Question

10. The demand of a product is given by p= -004 +100 + 200 and the cost for the product is given by C = 8 +2009 + 120000, where is the number of units sold a Find the quantity that maximizes profit and verify that it is a maximum b. What is the maximum profit?

Answer 1

To Given demand (P) = -0.004q3 + 1092 +200 Cast (c) 893 + 2009 +1220000 Revenue R = (p) (9) R= (-0.004 93 + 1098 +200) A R = 0.004q+ + 10% + 2009) a) profft p(q) = R(q)- (09) p(q) = (-0-00 494 +093+2009) -(89342009 + 120000) = -0.004qt toq3 +2009 -8q3 - 2009 - 120000 = -0.00 494 +293-120000 "P(q) = -0.004 94 +293 - 120000) To maximizes the profit, when plaq) =o. (4 CM anani pl(q) = 1 (-0004 94 + 2q3 – 120000] = +0.004) (493) +2(392) - = -0.06q3 +692 p(q) =0] -0.016 q3 + 6q2 =0 92 (-0.0169 +6)=0 52=0 (1) 6-0.0169 20 G= 0.016q This is not taken 9 - 016 = 375 for maximum profit. 2 = 375 q=375) that manimizes the proft ✓

b) Maxtonom profit ocors at quantity (q=375) PC9)|-375 = 60004) (375)+ + 2(375)3 - 120000 = -7.9101X107 + 1.05468x103 - 120000 24.4 262471875 X107 = maximum profpt = 2624 7187.5 26247187.5 (1) 2.6247 1875 Xlot)