If a company charges x dollars per item, it finds that it can sell 1500 - 3x of them. Each item costs $8 to produce.

(a) Express the revenue, R (x), as the function of price.

(b) Express the cost, C (x), as a function of price.

(c) Express the profit, P (x), which is revenue minus cost, as a function of price.

Step-by-step explanation:

According to that the number of produced items is (1500-3x) where x is the price

(a) the revenue is price*production

(1500-3x) x = 1500x-3x^2

(b) the cost is unitary cost*production

8x

(c) the profit is revenue - cost

1500x-3x^2 - 8x = 1492x - 3x^2

And according to that maximum profit is reached when the price is $249