Until recently, hamburgers at the city sports arena cost $ 2.50 each. The food concessionaire sold an average of 750 hamburgers on game night. When the price was raised to $ 3.20, hamburger sales dropped off to an average of 400 per night. The concessionaire's fixed costs were $333.00 per night and the variable cost was $1.48 per hamburger. A) Assume that the relationship between price p and demand x is linear. Express p as a function of x and find the domain of this function.
B) Find the revenue function in terms of x and state its domain.
C) Assume that the cost function is linear. Express the cost function in terms of x.
D) Graph the cost function and the revenue function in the same coordinate system.
E) Find the profit function in terms of
F) Evaluate the marginal profit at x=600 and interpret the results.
1) At a production level of 600 hamburgers, the profit is increasing at a rate of $per hamburger.
2) At a production level of 600 hamburgers, the profit is decreasing at a rate of $per hamburger.