Radmore Memorial Hospital has a problem in its fluids analysis lab. The lab has available three machines that analyze various fluid samples. Recently, the demand for analyzing blood samples has increased so much that the lab director is having difficulty getting all the samples analyzed quickly enough and still completing the other fluid work that comes into the lab. The lab works with five types of blood specimens. Any machine can be used to process any of the specimens. However, the amount of time required by each machine varies depending on the type of specimen being analyzed. These times are summarized in the following table.

Each machine can be used a total of 8 hours a day. Blood samples collected on a given day arrive at the lab and are stored overnight and processed the next day. So, at the beginning of each day, the lab director must determine how to allocate the various samples to the machines for analysis. This morning, the lab has 80 type-1 specimens, 75 type-2 specimens, 80 type-3 specimens, 120 type-4 specimens, and 60 type-5 specimens awaiting processing. The lab director wants to know how many of each type of specimen should be analyzed on each machine to minimize the total time that the machines are devoted to analyzing blood samples.
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem and solve it using Solver.
c. What is the optimal solution?
d. How much processing time will be available on each machine if this solution is implemented?
e. How would the model and solution change if the lab director wanted to balance the use of each machine so that each machine were used approximately the same amount oftime?

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Required Specimen Processing Time in Minutes Specimen Type Machine 23 4 5 5 4 4 2 4