The marketing team at widgets inc. is trying to determine the optimal price for a new product it has recently developed, code named "the unicorn." management estimates that at a price of $49 per unit, it will sell 500,000 units. if it lowers the price to $44 it expects sales to increase to 750,000 million units, and at a price of $39 it anticipates sales of 900,000 million units. because "the unicorn" is based on entirely new technology, management expects there to be a learning/experience curve (i. e., production costs per unit will decline). at a production volume of 500,000 units, management forecasts average costs of $32 per unit. at a production level of 750,000 million units, costs will average $29 per unit; and at production volume of 900,000 million units costs should average $27 per unit. fixed costs will total $7.5 million per year, regardless of the level of production. with this information in mind, what is the optimal price for the new product? show your work and explain.

Blue computers, a major pc manufacturer in the united states, currently has plants in kentucky and pennsylvania. the kentucky plant has a capacity of 1 million units a year and the pennsylvania plant has a capacity of 1.5 million units a year. the firm divides the united states into five markets: northeast, southeast, midwest, south, and west. each pc sells for $1,000. the firm anticipates a 50 perc~nt growth in demand (in each region) this year (after which demand will stabilize) and wants to build a plant with a capacity of 1.5 million units per year to accommodate the growth. potential sites being considered are in north carolina and california. currently the firm pays federal, state, and local taxes on the income from each plant. federal taxes are 20 percent of income, and all state and local taxes are 7 percent of income in each state. north carolina has offered to reduce taxes for the next 10 years from 7 percent to 2 percent. blue computers would like to take the tax break into consideration when planning its network. consider income over the next 10 years in your analysis. assume that all costs remain unchanged over the 10 years. use a discount factor of 0.1 for your analysis. annual fixed costs, production and shipping costs per unit, and current regional demand (before the 50 percent growth) are shown in table 5-13. (a) if blue computers sets an objective of minimizing total fixed and variable costs, where should they build the new plant? how should the network be structured? (b) if blue computers sets an objective of maximizing after-tax profits, where should they build the new plant? how should the network be structured? variable production and shipping cost ($/unit) annual fixed cost northeast southeast midwest south west (million$) kentucky 185 180 175 175 200 150 pennsylvania 170 190 180 200 220 200 n. carolina 180 180 185 185 215 150 california 220 220 195 195 175 150 demand ('000 units/month) 700 400 400 300 600