Explain/format as clearly as possible, please.

Q1. The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eatathon." The society will charge students $1.10 per serving of pasta. The society estimates that the total cost of producing x servings of pasta at the event will be

C(x) = 340 + 0.10x + 0.002x² dollars.

(a)Calculate the marginal revenue R'(x) and profit P'(x) functions.

R'(x) =

P'(x) =

(b)Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 200 servings of pasta (in $).

revenue $ _______

profit $ ____________

marginal revenue. $ _______ per additional plate

marginal profit. $ _______ per additional plate

The approximate [ ---Select--- profit /loss ] from the sale of the 201^st plate of pasta is $___?___ .

(c)For which value of x is the marginal profit zero?

x = ____?_____plates

The graph of the profit function is a parabola with a vertex at x = ____?___ , so the loss is at a minimum when you produce and sell ____?____ plates.

Q2. Given the following price-demand function, find the elasticity of demand, E(p), and determine whether demand is elastic, inelastic, or has unit elasticity for the following values of p. (Round your answers to two decimal places.)

x = 43,200 36p²

(a) p = 11

E(p) = ____?_____

• elastic
• inelastic
• unit elasticity

(b) p=24

E(p) = ___?____

• elastic
• inelastic
• unit elasticity

(c) p=20

E(p) ___?____

• elastic
• inelastic
• unit elasticity

Q3. The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by

x = (112 3p)²,

where p is the price per dumbbell, and x is the demand in weekly sales. Find the price Professor Schwarzenegger should charge for his dumbbells in order to maximize revenue. (Round your answer to the nearest cent.) $________

Q3. Assume that the price of a pair of running shoes is $78 and E(78) = 0.48. If the price is increased by $9, then what is the approximate change in demand? Round your answer to the nearest hundredth of a percent. The demand will [ ---Select--- increase decrease ] by approximately ____?____ %.