QM 350
Operations Research
Chapter 2
1.
A company produces two products that are processed on two assembly lines.
Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours.
Each product requires 10 hours of processing time on line 1, while on line 2 product 1
requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit,
and the profit for product 2 is $4 per unit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
2.
The Munchies Cereal Company makes a cereal from several ingredients. Two of the
ingredients, oats and rice, provide vitamins A and B. The company wants to know how
many ounces of oats and rice it should include in each box of cereal to meet the
minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B
while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1
milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2
milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
c. What would be the effect on the optimal solution if the cost of rice increased
from $0.03 per ounce to $0.06 per ounce?
3.
A canning company produces two sizes of cansregular and large. The cans are
produced in 10,000-can lots. The cans are processed through a stamping operation and
a coating operation. The company has 30 days available for both stamping and
coating. A lot of regular-size cans requires 2 days to stamp and 4 days to coat, whereas
a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size
cans earns $800 profit, and a lot of large-size cans earns $900 profit. In order to fulfill
its obligations under a shipping contract, the company must produce at least nine lots.
The company wants to determine the number of lots to produce of each size can (x1
and x2) in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
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4.
Solve the following linear programming model graphically and explain the solution
result:
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