A manufacturer of tennis rackets finds that the total cost of manufacturing x rackets/day is given by 0.0003x2 + 4x + 500 dollars. Each racket can be sold at a price of p dollars, where p = −0.0002x + 9 Find an expression giving the daily profit P for the manufacturer, assuming that all the rackets manufactured can be sold. Hint: The total revenue is given by the total number of rackets sold multiplied by the price of each racket. The profit is given by revenue minus cost. (Simplify your answer completely.)

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Jseberrio Jseberrio · Answer 1 · 2019-09-12T05:27:35+02:00

Answer:

[tex]PT =-0.0005^2 +5x - 500[/tex]

Step-by-step explanation:

We have price (P) = [tex]-0.0002x + 9[/tex]

to calculate Total revenue (TR) we have to multiply Price by Production quantity.

[tex]TR=P * X[/tex] , we denote production quantity with the letter X.

[tex] TR=(-0.0002x + 9)*x[/tex]

We apply distributive law and then we have:

[tex] TR=-0.0002x^2 + 9x[/tex] , this is the Total revenue (TR) of selling X amount of production at a P price.

Now we only have to find the Profit (PT) using the formula:

[tex]PT=TR - TC[/tex] , TR is total revenue and TC is total cost

The expression of the daily profit (PT) for the manufacturer is:

[tex] PT=-0.0002x^2 + 9x - (0.0003x^2 + 4x + 500)[/tex]

[tex] PT= - 0.0002^2 + 9x -0.0003^2 -4x -500[/tex]

[tex]PT =-0.0005^2 +5x - 500[/tex]