A). A maker of smartphones makes a profit of $140 on the sale of each phone that will be produced in 2019. The marketing department estimates that for each $20 of rebate, sales would increase by 16%. 1. How big should the rebate be in order to maximize the profit? Use the five-step method, as a modeling technique use one-variable optimization. 2. How sensitive is the answer to the 16% assumption? Calculate the sensitivities for both the amount of the rebate and the overall profit. 3. What if the marketing department is wrong and the rebate actually generates only 7% in additional sales per $20? 4. Can it happen that a rebate offer leads to a reduction in profit? A). A maker of smartphones makes a profit of $140 on the sale of each phone that will be produced in 2019. The marketing department estimates that for each $20 of rebate, sales would increase by 16%. 1. How big should the rebate be in order to maximize the profit? Use the five-step method, as a modeling technique use one-variable optimization. 2. How sensitive is the answer to the 16% assumption? Calculate the sensitivities for both the amount of the rebate and the overall profit. 3. What if the marketing department is wrong and the rebate actually generates only 7% in additional sales per $20? 4. Can it happen that a rebate offer leads to a reduction in profit