Question

A company produces two types of solar panels per​ year: x thousand of type A and y thousand of type B. The revenue and cost​equations, in millions of​ dollars, for the year are given as follows. R(x,y)=4x+5y C(x,y)= x^2- 2xy+ 7y^2 +6x - 93y - 8

Determine how many of each type of solar panel should be produced per year to maximize profit.

Part 1-The company will achieve a maximum profit by selling ____ solar panels of type A and selling____solar panels of type B.

Part 2- The maximum Profit is $____million

Answer 1

The profit function P(x,y)= R(x,y)- C(x,y) then find the critical point ( a,b) of the function P(x,y). Let D= P_{​​​​​​xx}​​​​ (x,y) P_yy(x,y)- P_​xy​(x,y). Evaluate its value at the critical point(a,b) as explained in the solution provided below.