Question

2. (3 points) A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 90 – x dollars per unit of A and q = 60 – y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = + 2xy + y? What should x and y be to maximize profit? What is this maximum profit (include units)?

Answer 1

P dollars Revenuc OF selling a unity for pa a dollars Revenue selling yunity for total revenue . petay. we know that and a=60-y. Given P=90-2 total revenue = (90-2) x + (60-4) y R(2, 4) = 90x - x² +604-22 R(2,7) - – x² - y² + +90x +604 function x²+2xy + y2 joint Cont Given Function Revenue protit function = cost tunction P(a,y) = – xy² +90x+607 -u-ray-22 p(x,y) = – 2x² – 28²-22y +902 + 60 so y the profit In order to d (p(2,4) and deplay) - 0 da dy mazimise .-2(2x)-27 (1) 4900 and -2(2), 2x +60=0 -48-2y +90 = 0 - uy-22 +60=0 2x + 4y - 60 2 untzy 90 - 0

By Eq - and solving 2x &q-0 » 42/+ ual+ 8y = 120 90 Yety by 30 y = 5 substitute y=5 in Eq - 0 4x +2y =90 4x + 10 - 90. 42 SO x = 20 and The Company Connell 20 unity of a unig of B maximum profit P(20,5) = -2 (2012-2(5)-2 (20)(5) +90x20+60 X5 P(20,5) = 105o So mazimum profit for Company is $ 1050 -