The government decided on opening new grant scheme for pharmaceutical research aiming to support the development of new drugs that eventually reduce the yearly budget the government allocates to drug subsidies for blood related diseases. Each university will not be allowed to ask for more than $1.7 million of funding overall (for all different grants from this Uni.). An internal committee at Wales University received 6 different grant proposals. They need to decide which of these proposals to be sent for the government competition. The amount asked for each of the 6 grants and the estimated saving amounts for the government is given bellow. See picture 2
The Wales committee think that it is possible to estimate the probability of the selection of the grant proposal by the government as a function of the number of young researchers allocated to work on the proposed grant and the past years success coefficient of the leading professor. The success coefficients of the leading professors associated with each grant are 3.1, 2.5, 4.5, 5.6, 8.2 and 8.5 for grants 1 to 6, respectively.
The exact formula for the probability is "The number of Young Researcher"/ "The number of young researcher" + "the success coefficient".
Another limitation of the Wales committee is that Faculty of Pharmacy has no more than 25 young researchers.
1. Develop a model to help to Wales committee decide which grant to select for the government scheme and how many of the young researchers to include in each grant proposal. (Wales University is interested to save government's drug subsidies as a result of research conducted in Wales).
2. Which grant proposals should Wales committee submit for the government scheme?
3. How many young researchers to include in each of the selected grant proposals?
Hint: it is a non-linear problem. Make sure you use multi-starts, as the initial solution plays a crucial role for non-linear problems. To increase the chances to get the best solution, rerun the model once again after receiving the first optimal solution.
Answer the question on a worddocs. Present your answers and working to each question in a excel spreadsheet.