Total Score
Name , Surname:…………………….…….
Number :…………………………………….….
DEPARTMENT OF MANAGEMENT
QUANTITATIVE METHODS MIDTERM EXAM
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1. The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected
profit is $6 per unit on special risk insurance and $4 per unit on mortgages. Management wishes to establish sales quotas for
the new product lines to maximize total expected profit. The work requirements are as follows:
Work-Hours per Unit
Work-Hours
Available
SpecialRisk Mortgage
Underwriting
3
2
1800
Administration
1
2
800
Formulate a linear programming model and use graphical method to solve this model.
Department
Solution:
2. The dietitian at a local penal institution is preparing the menu for tonight's light meal. Two food items will be served at the meal. The
dietitian is concerned about achieving the minimum daily requirement of two vitamins. The table given below summarizes vitamin
content per ounce of each food, the minimum daily requirements of each, and cost per ounce of each food. If xj equals the number of
ounces of food j:
Minimum
Food 1
mg/oz
Food 2
mg/oz
Vitamin 1
3
4
24 mg
Vitamin 2
4
2
20 mg
Cost per oz
$ 0,2
$ 0.4
Daily
Requirement
Find the minimum amount of foods that will minimize cost with graphical method.
Solution:
3. The Gutchi Company manufactures purses, and backpacks. The construction includes leather and the production process requires
sewing. The following table gives the availability of the resources, their usage by the two products, and the profits per unit.
Resource requirements per unit
Resource
2
Leather (ft )
a.
b.
c.
Purse
Bag
Daily availability
2
4
40 ft
28 hr
Sewing (hr)
2
1
Selling price ($)
24
20
Write the objective function and constraints.
Convert the inequalities into equations with slack variables.
Find the optimum solution with simplex method.
Solution:
2
4.
Minimize C =60x1 + 30x2
subject to 3x1+ x2 ≥ 24
x1 +x2 ≥ 16
x1,x2 ≥ 0
Solve the minimization problem, by converting to dual, with simplex method.
Solution:
5. Education: resource allocation. A metropolitan school district has two high schools that are overcrowded and two that are under
enrolled. In order to balance the enrollment, the school board has decided to bus students from the overcrowded schools to the under
enrolled schools. North Division High School has 300 more students than it should have, and South Division High School has 500 more
students than it should have. Central High School can accommodate 400 additional students, and Washington High School can
accommodate 500 additional students. The weekly cost of busing a student from North Division to Central is $5, from North Division to
Washington is $2, from South Division to Central is $3, and from South Division to Washington is $4. Determine the number of students
that should be bused from each of the overcrowded schools to each of the under enrolled schools in order to balance the enrollment and
minimize the cost of busing the students.
a.
b.
Write the consraints in equation form;
Form the matrix with big M method.
Solution: