Answer Happy

Andy Mendoza makes handcrafted dolls, which he sells at
craft fairs. He is considering mass-producing the dolls to sell in
stores. He estimates that the initial investment for plant and
equipment will be $15,000, while labor, materials, packaging, and
shipping will be about $4 per doll. He has determined that monthly
sales volume is related to price, according to the following
equation:
v = 2000 − 40p
(a) Develop the nonlinear profit function as a function of
price.
(b) Find the optimal price, the optimal volume per month, and
the maximal profit per month.
(c) Graphically show the nonlinear curve of the profit function
in (a) considering the optimal price and the maximal profit
obtained in (b). (You can use any software/websites to draw, or
only do it by hand).
(d) Explain the effect on the maximal profit in (b) when a new
constraint p ≤ 25 is added.
(e) Find the optimal price, the optimal volume, and the maximal
profit per month with a new relationship between volume and price
as v = 1000 − 20p + (10000/p)