Question

Write the profi t function for the given expense and revenue functions.

9. E = –12,500p + 78,000 R = –1,450p2 + 55,000p

Answer 1

To write the profit function, simply subtract the expense function E from the revenue function R. The resulting profit function P is given by P = -1,450p² + 67,500p - 78,000, which expresses profit as a function of the quantity of products sold (p).

Step-by-step explanation:

To write the profit function, we need to subtract the expense function (E) from the revenue function (R). You've been given the expense function E = –12,500p + 78,000 and the revenue function R = –1,450p² + 55,000p. So, the profit function (P) is obtained by:

• First write down the revenue function
• Then subtracting the expense function from the revenue function

Thus, the profit function P is:

P = R - E

P = (–1,450p² + 55,000p) - (–12,500p + 78,000)

Now we simplify the equation:

P = –1,450p² + 55,000p + 12,500p - 78,000

Combine like terms:

P = –1,450p² + (55,000p + 12,500p) - 78,000

P = –1,450p² + 67,500p - 78,000

This is the profit function that shows the profit depending on the number of products sold (p).