Operations Management (33:136:386:22-26) Spring 2025
Homework 1 – Due February 12th, Wednesday 11:50pm
Instructions: All questions are from the textbook. Please submit over the Canvas website as a pdf or a word document. Other formats such as .jpg, .dvi, .eps will not be accepted as it makes the grading difficult, and sometimes impossible in the blackboard grading system. You could also write your homework in hardcopy and scan it. There are some free smart phone applications that would allow you scan your homework if needed. Please do not forget to define decision and the slack variables properly. Explain your work in detail to get full credit. For fairness reasons, late homeworks will be subject to a penalty of 5 points per hour of delay. Please make sure that the format of the homework is correct, because if the submitted files cannot be opened by a pdf viewer, we will not be able to accept resubmissions.
1. (50 points) Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $64 per day, and a temporary operator is paid $42 per day. The company wants to determine the number of permanent and temporary operators to hire in order to minimize costs.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
2. (50 points) A canning company produces two sizes of cans—regular 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 ( and ) in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
3. (Bonus: 20 points) The Valley Wine Company produces two kinds of wine—Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A 1,000-gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing time. A batch of each type of wine requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of wine is limited to seven batches. The profit for a batch of Nectar is $9,000, and the profit for a batch of Red is $12,000. The company wants to determine the number of 1,000-gallon batches of Nectar and Red to produce in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
c. How much processing time will be left unused at the optimal solution?
d. What would be the effect on the optimal solution of increasing the available storage space from 50 to 60 cubic yards?
4. (Bonus: 20 points). Excel problem “Julia’s Food Booth” from the book on page 113.