Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an...

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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 $1,115.40 per night and the variable cost was $0.36 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. 1 p= 500 The domain of p is 0x2,000. (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x) = -X+4 The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 24x +9,750 and R(x) = 200x -0.4x for 0x500. (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0x500. Find the break-even points. Find the x-intercepts of the graph of P(x). (A) R(x) has a horizontal tangent line at x = 250. (B) The profit function P(x)= -0.4x + 176x-9750. (C) P(x) has a horizontal tangent line at x = 220. (D) Choose the correct graph of C(x), R(x), and P(x) graphed together. 25000- R(x) R(x) R(x) 25000- 25000- (x) C(x) 18750- 15750- A A A $750- 2 P(x) 9750- 5000+ P(x) 9750- 5000+ P(x) 250 250 250 9750- 5000- 0 500 B. What are the break-even points? A. (65,11310) and (319,18750) B. (65,11310) and (375,18750) C. (98,10631) and (319,16875) D. (130,12441) and (319,18750) E. (65,12441) and (319,21563) 0 The x-intercepts of the graph of P(x) occur at x = (Use a comma to separate answers as needed.) 500 0 X 500 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 $1,115.40 per night and the variable cost was $0.36 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. 1 p= 500 The domain of p is 0x2,000. (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x) = -X+4 The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 24x +9,750 and R(x) = 200x -0.4x for 0x500. (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0x500. Find the break-even points. Find the x-intercepts of the graph of P(x). (A) R(x) has a horizontal tangent line at x = 250. (B) The profit function P(x)= -0.4x + 176x-9750. (C) P(x) has a horizontal tangent line at x = 220. (D) Choose the correct graph of C(x), R(x), and P(x) graphed together. 25000- R(x) R(x) R(x) 25000- 25000- (x) C(x) 18750- 15750- A A A $750- 2 P(x) 9750- 5000+ P(x) 9750- 5000+ P(x) 250 250 250 9750- 5000- 0 500 B. What are the break-even points? A. (65,11310) and (319,18750) B. (65,11310) and (375,18750) C. (98,10631) and (319,16875) D. (130,12441) and (319,18750) E. (65,12441) and (319,21563) 0 The x-intercepts of the graph of P(x) occur at x = (Use a comma to separate answers as needed.) 500 0 X 500