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Course Number & Title: MGT4310  Operations Management HOMEWORK 2 THERE ARE FOUR PROBLEMS

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Course Number & Title: MGT4310  Operations Management

HOMEWORK 2

THERE ARE FOUR PROBLEMS.

1.  The Bluegrass Distillery produces custom-blended whiskey. A particular blend consists of rye and bourbon whiskey. The company has received an order for a minimum of 300 gallons of the custom blend. The customer specified that the order must contain at least 40% rye and not more than 280 gallons of bourbon. The customer also specified that the blend should be mixed in the ratio of rye to bourbon as 2 to 1 (i.e. rye:bourbon=2:1). The distillery can produce 500 gallons per week, regardless of the blend. The production manager wants to complete the order in 1 week. The blend is sold for $5 per gallon. The distillery company’s cost per gallon is $2 for rye and $1.5 for bourbon. The company wants to determine the blend mix that will meet customer requirements and maximize profits. 

1. Formulate a linear programming model for this problem.
2. Solve the problem by using the computer.

2.  Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 2.8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $3.0 per yard of denim and $4.0 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. 

1. Formulate a linear programming model for this problem. 
2. Solve the problem by using the computer.
3. How much extra cotton, processing time, and the demand for corduroy are left over at the             optimal solution in (a)? 
4. What is the effect on the optimal solution if the profit per yard of denim is increased from           $3.0 to $4.0?

3. A linear programming problem is given as follows:

 

maximize      ?  

Subject to               

 

1. Transform the problem into standard form.
2. Solve the problem by using the computer.
3. What is the effect on the optimal solution if the 2^nd constraint were discarded from the formulation?

4. Below tables show the Answer Report and the Sensitivity Report of the optimization problem.

Based on these two tables, answer the following questions.

1. Write the objective function.
2. What is the z value (objective function’s value)

2. Identify the sensitivity ranges for the objective function.
3. Write the constraint quantity values.
4. Identify the sensitivity ranges for the constraint quantity values.
5. What is the unknown shadow price? (Shown as yellow)
6. Why are there 4 shadow prices?