12. Project Planning. An architectural design firm is faced with a decision as to which projects to bid on for the coming year. Ten projects are available for which they are qualified. The following table lists the profit they can expect to make from each project, as well as the initial investment they will have to make and the design time required. They cannot afford to invest more than $55,000 or use more than a total of 1,000 hours of design time. Their objective is to choose those projects that will maxi- mize their expected profit. Profit Investment Design time Project ($000) ($000) (hours) 55 6.2 123 75 8.8 145 98 8.4 164 67 5.9 135 78 6.9 153 82 8.9 122 51 6.7 87 90 9.2 145 76 6.1 137 10 69 6.0 143 a. Assuming no uncertainty in profits, investment, or design time, what is the maximum profit the firm can achieve, and which projects should it select? Note: this solution must not use more investment capital or design time than is available. b. Represent the uncertainty in profits, investment, and design time using normal distributions, with standard devia- tions of 5 percent of the mean for profit, 10 percent for the initial investment, and 15 percent for design time. Determine the maximum expected profit the firm can achieve under these assumptions, and which projects it should select. Note: this solution must be such that the investment and design time constraints are violated no more than 5 percent of the time