Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 1,500 hamburgers on game night. When the price was raised to $3.20, hamburger sales dropped off to an average of 800 per night. The concessionaire's fixed costs were $1,162.80 per night and the variable cost was $1.21 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= 4-0.001x The domain of p is 0≤x≤4000 (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x)= -0.001x² + 4x The domain of R(x) is 0≤x≤4000 (Type a compound inequality.) (C) Assume that the cost function is linear. Express the cost function in terms of x. C(x) =

11. A company that manufactures ski jackets estimates that their fixed costs are $21,900 and variable costs of $24 per jacket. A survey indicates that a price of $140 results in a demand of demand of 300 jackets and that a price of $100 will result in a demand of 500 jackets. a) Find the price-demand equation assuming a linear relationship b) Find the revenue function and determine the domain its domain using the price-demand equation c) Find the total cost function d) Find the profit function and the marginal profit function e) Evaluate the marginal profit at production levels of 300 and 600 jackets and interpret your result being specific about quantities, units, and increasing/decreasing f) Determine the break-even points

The total cost function is given by the fixed costs minus the variable costs. True False

Assume that the linear cost model applies. If the total cost of producing 200 items at $5 each is $1690, find the cost equation. (Let x be the number of items.)C(x) =