Answer:
The company will achieve a maximum profit by selling 7000 solar panels of type A and 9000 solar panels of type B.
The maximum profit is $412 million.
Explanation:
Profit is the revenue minus the cost.
P(x,y) = R(x,y) − C(x,y)
P(x,y) = (3x + 2y) − (x² − 2xy + 6y² + 7x − 92y − 3)
P(x,y) = 3x + 2y − x² + 2xy − 6y² − 7x + 92y + 3
P(x,y) = -x² − 6y² + 2xy − 4x + 94y + 3
To maximize, find the partial derivatives and set to 0.
∂P/∂x = -2x + 2y − 4
∂P/∂y = -12y + 2x + 94
0 = -2x + 2y − 4
0 = -12y + 2x + 94
--------------------------
0 = -10y + 90
y = 9
x = 7
Evaluate P(x,y) at (7,9):
P(7,9) = -(7)² − 6(9)² + 2(7)(9) − 4(7) + 94(9) + 3
P(7,9) = -49 − 486 + 126 − 28 + 846 + 3
P(7,9) = 412
The company will achieve a maximum profit by selling 7000 solar panels of type A and 9000 solar panels of type B.
The maximum profit is $412 million.