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A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ax, y)-2x2-2xy + y2-9x-10y + 11 R(x, y)-7x+6y Find the number of each type of product that should be manufactured to maximize profit. thousand units thousand units What is the maximum profit?



Answer :

The value of x is 16 and the value of y is 24. The maximum profit is 309,000 dollars.

C(x,y) = 2x²-2xy+y²-9x-10y+11

R(x,y) = 7x+6y

Profit function P(x,y) = R(x,y) - C(x,y)

= 7x+6y - (2x²-2xy+y²-9x-10y+11)

= -2x²-y²+16x+16y+2xy-11

P(x) = -4x+16+2y

P(y) = -2y+16+2x

P(x) = 0

P(y) = 0

-4x+16+2y = 0

-2y+16+2x = 0

-2x+32 = 0

x = 16

y = 24

P(16,24) = 304

Hence the maximum profit is 304,000.

To learn more about profit and loss,

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