Question

A print shop makes bumper stickers for election campaigns. If x stickers are ordered (where x < 10,000), then the price per sticker is 0.14 − 0.000002x dollars, and the total cost of producing the order is 0.091x − 0.0000005x2 dollars. Use the fact that profit = revenue − cost to express P(x), the profit on an order of x stickers, as a difference of two functions of x.

Answer 1

Answer:

P(x) = (0.049x - 0.0000015x²)

Step-by-step explanation:

price per sticker is 0.14 − 0.000002x dollars

total cost of producing the order is 0.091x − 0.0000005x² dollars.

P(x) = profit = Revenue - Cost

Let the number of units of stickers made be x

Revenue = (price per sticker) × (total units sold) = (0.14 − 0.000002x) × (x)

= (0.14x - 0.000002x²) dollars.

Cost of producing x units in the order = (0.091x − 0.0000005x²)

P(x) = 0.14x - 0.000002x² - (0.091x − 0.0000005x²) = 0.14x - 0.091x - 0.000002x² + 0.0000005x²

= (0.049x - 0.0000015x²)

P(x) = (0.049x - 0.0000015x²)

Hope this Helps!!!

Answer 2

The  profit on an order of x stickers, as a difference of two functions of x is:

$P(x) = (0.049x - 0.0000015x^2)$

As Profit( P(x)) = Revenue - Cost

We have price per sticker = 0.14 − 0.000002x dollars

Total cost of producing the order = 0.091x − 0.0000005x² dollars.

 Let x number of units of stickers be made.

Then,

Revenue = (price per sticker) × (total units sold)

= (0.14 − 0.000002x) × (x)

= (0.14x - 0.000002x²) dollars.

And, Cost of producing x units in the order = (0.091x − 0.0000005x²)

$P(x) = 0.14x - 0.000002x^2 - (0.091x − 0.0000005x^2)\\= 0.14x - 0.091x - 0.000002x^2 + 0.0000005x^2\\= (0.049x - 0.0000015x^2)\\P(x) = (0.049x - 0.0000015x^2)$

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