Operations Management. Please do ONLY (e) and show how solution was solved via algebra. Thank you.

3. Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering massproducing 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=200040p (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). (d) Explain the effect on the maximal profit in (b) when a new constraint p25 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=100020p+p10000