Question

The reverus trom soting eq itens is R(q)=300q−q 2and the total cost it C(q)=75+8q. Write a function that gives the total profit earned. and fod the quantify which maximizes the profit. Profit π(Q)=

Answer 1

The total profit is calculated by subtracting the total cost from the total revenue. The profit function can be written as -Q^2 + 292Q - 75. The quantity that maximizes the profit is 146.

Step-by-step explanation:

To find the total profit earned, we subtract the total cost from the total revenue. Let's denote the total profit as π(Q). From the given information, the total revenue (R(Q)) is 300Q - Q^2 and the total cost (C(Q)) is 75 + 8Q. Therefore, we have:

π(Q) = R(Q) - C(Q)

π(Q) = (300Q - Q^2) - (75 + 8Q)

π(Q) = -Q^2 + 292Q - 75

To find the quantity that maximizes the profit, we can find the vertex of the quadratic equation -Q^2 + 292Q - 75. The x-coordinate of the vertex gives us the quantity that maximizes the profit. We can use the formula x = -b/2a to find it. In this case, a = -1 and b = 292. Substituting these values into the formula, we get:

x = -292/(-2)

x = 146

Therefore, the quantity Q = 146 maximizes the profit.