A tree farm cultivates Virginia pine trees for sale as Christmas trees. Pine trees, being what they are, require extensive pruning during the growing season to shape the trees appropriately for the Christmas tree market. For this purpose, the farm manager can purchase pruning hooks for $16.60 each. He also has a ready supply of spears (at $3 each) that can be bent into pruning hooks. This conversion process requires 1 hour of labor, whereas final assembly of a purchased pruning hook takes only 15 minutes of labor. Only 10 hours of labor are available to the manager. With labor rates at $8.40 per hour, the farm manager intends to spend no more than $280 on buying or making pruning hooks this year. Given these limitations, and assuming fractional solutions are acceptable for parts (a) through (d), answer the following:
a) Formulate a linear program to find how many pruning hooks can he acquire (from outright purchase and through conversion).
b) Implement your formulation in Excel and use Solver to find the optimal solution. Provide answers for the optimal amounts and the corresponding total objective function value. Provide an organized screen shot of your solution.
c) Using sensitivity analysis, if the manager can secure 4 more hours of labor, how many more hooks can be obtained. Provide an answer based on the sensitivity report without resolving the model. Show your work and justify your solution.
d) Using sensitivity analysis, if the manager can secure an additional $100 but with the same number of original hours how many more hooks can he maximum have? Provide an answer based on the sensitivity report without resolving the model. Show your work and justify your solution.
e) If the numbers of hooks must be integers, what additional constraints need to be added to the formulation. Implement your integer formulation in Excel and use Solver to find the new optimal solution as an integer linear program.
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