MODEL FORMULATION AND GRAPHICAL SOLUTION PROBLEMS

The problems/questions below must be answered by using these steps:
a. Formulate linear program
b. Calculate constraint intercepts
c. Graph Lines
d. Use test values to find feasible region
e. Identify corner points
f. Substitute corner points into objective function
g. Identify the solution
__________________________________________________________________________
1. Shirt shop makes t-shirts with logos and sells them in its chain of retail store. It contracts with two different plants-one in Puerto Rico and one in the Bahamas, the shirts from the plant in Puerto Rico coast $.0.46 apiece, and 9% of them are defective and can't be sold. The shirts from the Bahamas cost only $0.35 each, but they have an 18% defective rate, Shirt shop needs 3,500 shirts. To retain its relationship with the two plants, it wants to order at least 1,000 shirts from each. It would also like at least 88% of the shirts it receives to be salable.

a. formulate a linear programming model for this problem
b. solve this model by using graphical analysis
__________________________________________________________________________
2. The admission office at Tech wants to determine how many in-state and out-of-state students to accept for next fall's entering freshman class. Tuition for an in-state student is $7,600 per year, whereas out-of-state tuition is $22,500 per year. A total of 12,800 in-state and 8,100 out-of-state freshmen have applied for next fall, and Tech does not want to accept more than 3,500 students. However, because the Tech is a state institution, the state mandates that it can accept no more than 40% out-of-state students. From past experience the admissions office knows that 12% of instate students and 24% of out-of state students will drop out during their first year. Tech wants to MAXIMIZE total tuition while limiting the total attrition to 600 first year students.

a. formulate a liner programming model for this problem
b. Solve this model by using graphical analysis