Calculate the price elasticity of demand for roses

Question

Monopoly Pricing and Output:

Shelley works at University florist in Minneapolis. Every Friday night, the owner of the florist shop gives her the unsold inventory of roses at no cost, which Shelley then sells on Riverside Avenue to pedestrians and motorists. Shelley has a monopoly on rose sales in this area, and faces a demand curve given by:

Inverse Demand: p = 40 - q^d

where p represents the price in dollars of a dozen roses and q^d represents quantity demanded in dozens. For example, at a price of $10 per dozen roses, a quantity 30 dozen roses will be demanded.

NOTE:  The following formula may be used for the problem:

Total Revenue: TR(q) = p.q

Total Revenue: TR(q) = [40 - q] . q = 40.q - q²

Marginal Revenue MR(q) = ΔTR/Δq

Marginal Revenue MR(q) = 40 - 2.q

Price Elasticity of Demand: E^d_p = (Δq/Δp)(p/q)

Question 1: Calculate the price Shelley should charge as a profit-maximizing monopolist, the equilibrium quantity she will sell, and her profits. 

Question 2: At the profit-maximizing price and quantity, calculate the price elasticity of demand for roses. Is Shelley pricing on the inelastic portion of the demand curve?  Explain why or why not.