Question

Until recently, hamburgers at the city sports arena cost $ 2.50 each. The food concessionaire sold an average of 2250 hamburgers on game night. When the price was raised to $2.80 hamburger sales dropped off to an average of 2,100 per night. The concessionaire's fixed costs were $1725.20 per night and the variable cost was $1.70 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=

The domain of p is (Type a compound? inequality.)

(B) Find the revenue function in terms of x and state its domain.

R(x)=

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)=

(D) Graph the cost function and the revenue function in the same coordinate system.

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)=

(F) Evaluate the marginal profit at x=600 and interpret the results.

The marginal profit at x=150 is $:

a)At a production level of 150 hamburgers, the profit is decreasing at a rate of $ per hamburger.

b)At a production level of 150 hamburgers, the profit is increasing at a rate of $ per hamburger.

Answer 1