Tazer management now has concluded that the company cannotdevote enough money to research and development to undertake all ofthese projects. Only $1.5 billion is available, which may be notenough for all the projects. The first row of table shows theamount needed (in millions of dollars) for each of these projects.The second row estimates each project’s probability of beingsuccessful. If a project is successful, it is estimated that theresulting drug would generate the revenue shown in the third row.Thus, the expected revenue (in the statistical sense) froma potential drug is the product of its numbers in the second andthird rows, whereas its expected profit is this expectedrevenue minus the investment given in the first row. These expectedprofits are shown in the bottom row of table. The objective is tochoose the projects that will maximize the expected profit whilesatisfying the budget constraint.
a. Formulate algebraic form for this problem. (Please clearlydefine all the decision variables, clearly write down the objectivefunction and each constraints)
b. Formulate and solve this model on a spreadsheet.
TABLE Data for the Tazer Project SelectionProblem
| Project |
| 1 (Up) | 2 (Stable) | 3 (Choice) | 4 (Hope) | 5 (Release) |
| R&D investment ($million)* | 450 | 300 | 620 | 510 | 200 |
| Success rate | 60% | 30% | 30% | 20% | 45% |
| Revenue if successful ($million) | 1,400 | 1,200 | 2,200 | 3,000 | 600 |
