$4$

Answer the next five questions based on the case given below:

Tower Engineering Corporation is considering undertaking several proposed projects for the

next fiscal year. The projects, the number of engineers and the number of support personnel

required for each project, and the cost for each project are summarized in the following table:

Formulate an integer linear program that minimizes Tower's cost, subject to constraints,

which will be stated in the questions that follow. No more than $150$ engineers can be used.

Let $P_i=0$ or $1,$ indicate if project i will not be undertaken or will be undertaken respectively.

The most appropriate objective function for Tower Engineering Corporation is given as:

Max. $\}\{1\}+3\mathrm{.}4P2+2\mathrm{.}6P3+2\mathrm{.}8P4+3P5+2\mathrm{.}5P6$

Min. $\}\{1\}+3\mathrm{.}4P2+2\mathrm{.}6P3+2\mathrm{.}8P4+3P5+2\mathrm{.}5P6$

Max. $50$P$1+35$P$2+40$P$3+45$P$4+55$P$5+30$P$6$

Min. $50$P$1+35$P$2+40$P$3+45$P$4+55$P$5+30$P$6$