Operations Management (61 problems)

Suppose a quality control specification on a particular part allows at most 1% defectives. The company uses a sampling plan wherein 400 parts are examined, and if 8 or more are found to be defective, the lot is rejected. Construct a well-labeled power curve vs. p for this sampling plan. What is the exact a-level for the test when p = 0.01?

Suppose a quality control specification on a particular part allows at most 1% defectives. The company uses a sampling plan wherein 400 parts are examined, and if 8 or more are found to be defective, the lot is rejected. Construct a well-labeled power curve vs. p for this sampling plan. What is the exact powe of the test when pi = 0.01?

In the following table, if cell A3 is filled on the next iteration, what is the improvement in the objective function?

Consider the following transportation problem:

How many supply-side constraints are there? Write the supply-side constraints.

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work, however their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does what manuscript. Estimates of editing times (in hours) for each manuscript by each editor is:

What is the total minimum editing time?

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these trikes.

As indicated in the table below, the company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles, so it has arranged to purchase additional components, as necessary. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.

Let x₁ be the number of units to make and x₂ be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, what is the objective function?

RCA has a contract to supply 27-inch televisions to a national chain of stores specializing in electronic equipment. This contract calls for RCA to supply the numbers of TVs shown here. It costs RCA $100 to manufacture a TV in September or October; however because of an increase in labor costs, manufacturing costs will increase to $110 in November. RCA can manufacture more than it needs in any month, although the maximum production in any month is 1500 units. The cost of storing a TV is $10/month. That is, if a TV is made in October and shipped in November, the cost of storing the set for one month is $10. Find the optimal production schedule for RCA.

Month September October November December

Demand 800 1000 1400 1600

Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?

The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x₁), bright red nail polish (x₂), basil green nail polish(x₃), and basic pink nail polish(x₄) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that green nail polish does not require any time to prepare its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for fire red and green polish is 25 bottles, while constraint 4 specifies that the minimum demand for bright red, green and pink nail polish bottles combined is at least 50 bottles.

a) To what value can the per bottle profit on fire red nail polish drop before the solution (product mix) would change?

b) By how much can the per bottle profit on green basil nail polish increase before the solution (product mix) would change?

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next productions cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each and tables will result in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

What are the total monthly transportation costs for the optimal solution?

Student Enterprises sells two sizes of wall posters, a large 3X4 foot poster and a smaller 2X3 foot poster. The profit earned from the sale of each large poster is $3; each smaller poster earns $2. The firm, although profitable, is not large; it consists of one art student, Jan Meising, at the University of Kentucky. Because of her classroom schedule, Jan has the following weekly constraints: (1) up to three large posters can be sold, (2) up to five smaller posters can be sold, (3) up to 10 hours can be spent on posters during the week, with each large poster requiring 2 hours of work and each small one taking 1 hour. With the semester almost over, Jan plans on taking a three month summer vacation to England and doesn’t want to leave any unfinished posters behind. Find the integer solution that will maximize her profit.

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the constraint for malt?

Suppose your supervisor asks you to use the transportation method to rearrange the desks of everyone in the office. How would you do it? What other factors are important but will not be considered in the solution of the transportation table?

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

What are the supply constraints for the factories?

Consider the following transportation problem:

How many demand-side constraints are there? Write the demand-side constraints

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below.

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, develop the model that will maximize the number reached and achieve an exposure quality of at least 1000.

Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.

The profit for either model is $1000 per lot.

a. What is the linear programming model for this problem?

b. Find the optimal solution.

c. Will there be excess capacity in any resource?

Consider a capital budgeting example with 5 projects from which to select. Let x₁ = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Conditions are independent. Projects cost $100, $200, $150, $75, and $300 respectively. The budget is $450. Write the appropriate constraint for the following condition. If project 3 is chosen, project 4 must be chosen.