#35

Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 4,500 hamburgers on game night. When the price was raised to $3.00, hamburger sales dropped off to an averag of 4,000 per night. The concessionaire's fixed costs were $7,405.30 per night and the variable cost was $0.54 per hamburger. Answer the following questions (A) through (F) (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. p =(Simplify your answer.) The domain of p is .(Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x) =(Simplify your answer.) The domain of R(x) is .(Type a compound inequality.) (C) Assume that the cost function is linear. Express the cost function in terms of x. C(x) =(Simplify your answer.) (D) Graph the cost function and the revenue function in the same coordinate system. Choose the correct graph below. O A. O B. O C. O D. ARC ARC ARC 12 500- ARC 12.500 12 500- 12.500 Q Q Q 7.000 7.000 7.000 7.000Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 4,500 hamburgers on game night. When the price was raised to $3.00, hamburger sales dropped off to an average of 4,000 per night. The concessionaire's fixed costs were $7,405.30 per night and the variable cost was 50.54 per hamburger. Answer the following questions (A) through (F). 7,000 7.000 7,000 7.000 Find the break-even points. The break-even points are (Simplify your answer, Type an ordered pair, Use a comma to separate answers as needed ) (E) Find the profit function in terms of x. P(x) =(Simplify your answer.) (F) Evaluate the marginal profit at x = 4920 and interpret the results. The marginal profit at x = 4920 is $ (Simplify your answer.) Interpret the marginal profit. O A. At a production level of 4920 hamburgers, the profit is increasing at a rate of $ per hamburger O B. At a production level of 4920 hamburgers, the profit is decreasing at a rate of S per hamburger