EXERCISE 4: Solving simple linear programming problems Given the following linear programming formulation: Maximize LIE-00x1 + 3,000Jr2 Subject to: 40x1 + 25x2 5 80,000 (constraintl) 2024:1 + 30x2 5 60.000 (constraintZ) xyxz E 0 (non. negativity constraints). a] Solve the problem graphically. bl Solve the problem using Excel solver. c] What is the total objective lunction value? d} Do both variables contribute to the solution? Why? e] Does any variable have a slack value? If so, what does it mean? EXERCISE 5: Structuring and solving simple linear programming problems The cost of providing public services at a local hospital has been scrutinized by management. Although these services are used as marketing tools for the hospital, the cost and availability of scarce resources require their optimal allocation while minimizing costs. Two popular programs being assessed for this purpose are "Family Planning" [FF] and "Health - Drive - Screenings" {HDS}; their costs to the hospital for each offering are S200 and 5400, respectively. The health care manager in charge ol operations found three common patterns of resource consumption for each of these services and the available resources, shown in Table 3. Table 3 Resource Type FP HDS Available Resources per Month Staf-l time 50 120 430 minutes Materials 30 90 250 kits Rent space 1 3 occasions a] Formulate this as a linear programming problem. bl Solve the problem graphically. c] Solve the problem using Excel solver. d} In a given month, how many FF and how many HDS should be offered? e] With the proposed class offerings, how many kits will be left over [not distributed in the classes]? l'} what is the yearly cost of these two programs to the hospital