For this question, the solution that I keep getting is -268P+20023.4
My teacher’s solution shows that the answer should be -268P+19976.6
Can anyone help me figure out what I’m doing wrong, or is my teacher’s solution wrong?
3. (20 points) Suppose a ﬁrm’s inverse demand for their product is P = 200 — 4Q + 6A”,where Q is the number of units sold and A is the dollar amount spent on advertising. Further assume that the cost function for this ﬁrm is C(Q) = 2Q2 + 5Q. Determine theproﬁt maximizing level of sales and advertising expenditure. 2r=PQ—C(Q)—A7:2(200—4Q+6A"’5)Q—2Q2—5Q—A 7:” = 20¢)Q—4Q2 + 6QA0’5 —2Q2 —5Q— A7: =195Q — 6Q2 + 6QA"’S — A Take derivative with respect to Q and A and set equal to zero. al:l95—12Q+6A”’5=05Q a” 40,5 —=3 A —1=0 6A Q Solving for the two equations and two unknowns: Q* = 6.5 and A* =$380.25