DR.SAMULESON

10.1

Given the following linear programming formulation:

40x 1 +  25x 2 < 80,000(constraint 1)

20x 1 + 30x 2 < 60,000 (constraint 2)

x 1 + x 2 > 0 (non-negativity constraints

a)      Solve the problem graphically

b)      Solve the problem using excel solver

c)       What is the total objective function?

d)      Do both variables contribute to the solution? Why?

e)      Does any variable have a slack value? If so, what does that mean?

10.2

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 (FP) and Health drive screenings (HDS) their costs to the hospital each offering $200 and $400 respectively. The health care manager in charge of operations found three common patterns of resource consumption for each of these services and the available resources, Shown Table EX 10.2

Resource type           FP           HDS                     Available resources per month

Staff Time                   60           120                                            480 minutes

Materials                    30             90                                            250 kits

Rent Space                                   1                                              3 occassions

a)      Formulate this as a linear programming problem

b)      Solve this problem graphically

c)       Solve this problem using excel  solver

d)      In a given month how many FP and how many HDS should be offered?

e)      With that proposed class offerings, how many kits will be left over (not distributed in classes?)

f)       What is the yearly cost of these programs to the hospital?

10.4

A hospital is evaluating the feasibility of offerings among three technologies, on the basis of what would make the most profit. These new technologies are:

1. Closed chest by pass surgery  with daVinici surgery robot

2. Gamma Knife

3. Positron emission tomography (PET) scanner

Table EX 10.4 gives the information on profit, the amount of common resources used by each of the three technologies per case, and their available resources per month.

                                                                                                                                                          Available

                                                                   daVinici                Gamma Knife       PET                  Resources

Profit$                                                      $2,000                   $3,500                   $2,000

Total Staff Time                                       15                           12                            1.5                  2,000 hours

Maintenance                                            25                           25                           22                   1,500 minutes

Computer Resources                              20                            25                           10                   3,000 minutes

a)      Formulate this as a linear problem

b)      Solve this problem using Excel solver

c)       Based on optimal solution, which product(s) should be offered, and how many procedures can be offered in a month?

d)      What is the expected contribution of new technology to the hospital’s monthly profits?