I want to to solve this problem, the first pic is just example Math 206-0002 Spr

Question

I want to to solve this problem, the first pic is just example

Math 206-0002 Spring 2018 Homework: Sect 6.3 Save Score: 0.33 of 1 pt 3 of 3 (3 complete) HW Score: 77.78%, 2.33 of 3. & Bus Econ 6.3.15 Question Help 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)-6x + 7y c(x,y-x2-4xy + 7y2 + 12x-29y-4 Determine how many of each type of solar panel should be produced per year to maximize proft The company will achieve a maximum profit by selling 5,000 solar panels of type A and selling 4,000 solar panets of type B The maximum profit is $ 61 million. Question is complete. Tap on the red indicators to see incorrect answers. All parts showing Similar Question O Type here to search

Explanation / Answer

Sol:

P(x, y) = R(x, y) - C(x, y) = (5x + 7y) -(x^2 - 2xy + 7y^2 + 3x - 27y - 8)

Profit will be maximized when ?P/?x = ?P/?y = 0.

.. ?P/?x = 0 = 5 -2x +2y -3
.. ?P/?y = 0 = 7 +2x -14y +27
Simplifying these equations we have two equations in two unknowns:
.. => -2x+2y +2=0 => -x +y=-1
..=>2x-14y=-34 =>x-7y=-17
Subtracting the second from the first gives
.. -6y = -18
.. y = 3
Then
.. -x +y=-1 => x =1+y => x=4
The company will achieve a maximum profit by selling 4000 solar panels of type A and selling 3000 solar panels of type B.

The maximum profit is P(4, 3) = 20+21 -(16-24+63+12-81-8)= $63 million.

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