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.