webwork /math256spring18section2/14.7/15 14.7: Problem 15 Previous Problam Probl

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webwork /math256spring18section2/14.7/15 14.7: Problem 15 Previous Problam Problem List Noxt Problem Next Problem (1 point) A company operates two plants which manufacture the same item and whose total cost functions are c, 10 + 0.04q? and C2-3 + 0.0593. where q1 and q2 are the quantities produced by each plant. The total quantity demanded, q q1 +2 , is related to p 60 0.05q. How much should each plant produce in order to maximize the company's profit? 42 Adapted from M. Rosser, Basic Mathematics for Economists, p. 318 (New York: Routledge, 1993). Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining Email instructor

Explanation / Answer

Profit = Revenue -Cost

P(q1, q2) = (q1+q2)p?(C1+C2).

I will use x =q1 and y=q2 for conveneince.

P(x,y) = (x+y)(60 -0.05(x+y)) - (10+0.04x² +3+0.05y²)

P(x,y) =-0.09 x^2 - 0.1 x y + 60 x - 0.1 y^2 + 60 y - 13

Find partial derivative as

Px = -0.18 x - 0.1 y + 60

Py= -0.1 x - 0.2 y + 60

Now to find critical point, solve Px =0 and Py=0

-0.18 x - 0.1 y + 60 =0

-0.1 x - 0.2 y + 60 =0

This system of equation can be solved using algebra to obtain x =3000/13 and y =2400/13

which is about x = 230.769 and y =184.615

hence

q1 = 231

q2 =185

(round it as needed)

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