The Texas Electronics Company (TEC) is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all projects by the number of available scientists, which is 40, and the budget constraint, which is $300,000. Following are resource requirements and the estimated profits for each project: Project Expense($000) Scientists Required Profit ($000)
1 60 7 36
2 110 9 82
3 53 6 29
4 147 4 16
5 192 7 56
6 185 6 61
7 173 8 48
8 165 5 41
Formulate this problem using integer programming.
Solve it using excel. (Hint: in excel, assign integer constraint to decision variables by selecting "int" when selecting integer constraints)
What is the maximal profit? Which projects should be selected?
Suppose the management team decides that project 2 and project 5 are mutually exclusive, what it the revised formula? What is the revised maximal profit? What is the revised projected selected?
Suppose the management team also decides to undertake at least two of the projects involving consumers products (these happens to be projects 5-8). Then what is the revised formula? What is the revised maximal profit? What is the revised projected selected?

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.