A manufacturer of television sets makes two models, the Deluxe and the Standard.

Question

A manufacturer of television sets makes two models, the Deluxe and the Standard. The manager estimates that when x hundred Deluxe sets and y hundred Standard sets are produced each year, the annual profit will be:

The company can produce exactly 30,000 sets each year. How many Deluxe and Standard sets should be produced each year in order to maximize annual profit?

x: ________________ hundred deluxe sets

y: ________________ hundred standard sets

A manufacturer of television sets makes two models, the Deluxe and the Standard. The manager estimates that when x hundred Deluxe sets and y hundred Standard sets are produced each year, the annual profit will be: P(x,y)=-0.3x^2-0.3xy-0.5y^2+95x+125y-2500. The company can produce exactly 30,000 sets each year. How many Deluxe and Standard sets should be produced each year in order to maximize annual profit? x: ________________ hundred deluxe sets y: ________________ hundred standard sets

Explanation / Answer

x+y=300
y=300-x
substituiting in the function,

P(x)=-0.3x^2 -0.3x(300-x) -0.5(300-x)^2 +95x +125(300-x) -2500

dP/dx=-0.6x +0.6x -0.5[2(300-x)(-1)] +95 -125 =0

or, 300-x -30=0

or, x=270

y=30

Now i will be very sad if that also is not the answer :(

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