TimsTabletCo (TTC) produces tablet computers, and it must determine the number of units to be produced during each of the next four months. The following table gives the monthly demand and the monthly cost of producing each unit: Month 1 2 3 4 Demand (in units) 5000 2000 6000 1000 Production Cost (dollars per unit) 400 600 200 300 At the start, before Month 1, TTC has an inventory of 2000 units. Each month, up to 4000 units can be produced. TTC can use the units produced in a particular month in two ways: either use some units to satisfy the demand in the same month, or store some units in inventory for future use. The cost of storing units in inventory is $100 per unit per month. (a) Formulate an LP problem (P) to minimize the total cost of meeting the demands of the next four months. (b) Write the dual LP (D) of (P).

TimsTabletCo (TTC) produces tablet computers, and it must determine the number of units to be produced during each of the next four months. The following table gives the monthly demand and the monthly cost of producing each unit: Month 1 2 3 4 Demand (in units) 5000 2000 6000 1000 Production Cost (dollars per unit) 400 600 200 300 At the start, before Month 1, TTC has an inventory of 2000 units. Each month, up to 4000 units can be produced. TTC can use the units produced in a particular month in two ways: either use some units to satisfy the demand in the same month, or store some units in inventory for future use. The cost of storing units in inventory is $100 per unit per month. (a) Formulate an LP problem (P) to minimize the total cost of meeting the demands of the next four months. (b) Write the dual LP (D) of (P).

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter11: Linear Optimization Models

Section: Chapter Questions

Problem 13P: The Silver Star Bicycle Company will manufacture both mens and womens models for its Easy-Pedal...

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The Silver Star Bicycle Company will manufacture both mens and womens models for its Easy-Pedal bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 mens and 125 womens models to be shipped during the first month and 200 mens and 150 womens models to be shipped during the second month. Additional data are as follows: Last month, the company used a total of 1,000 hours of labor. The companys labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. (Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period + produced this period demand this period = inventory at end of this period.) a. Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained and what are the monthly labor requirements? b. If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule? How much will the cost increase? What would you recommend?
Neu Fabrication Company operates 360 days a year and uses 150 cartridges each day. Using a continuous inventory system, Neu orders 10,800 cartridges at a time. The orders are timed so that the new cartridges arrive just as inventory runs out (i.e. inventory level = 0), and replenishment is instantaneous. If Co= $1,400, what is the total ordering cost for all orders in a year (i.e. the Annual Ordering Cost)? O $1400 $7000 $2800 $500
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Resear Company sells modems. Resear desires to hold a finished goods inventory equal to 100% of the next month’s sales requirement of modems. The beginning finished goods inventory is 1,200 units. Forecasted unit sales for April and the next three months are as follows: April May June July 800 850 925 1,000 The production of one finished unit requires 5 pounds of raw material. The company desires to have a one-month supply of raw materials as the ending inventory for each month. The beginning inventory of raw materials is 6,190 pounds. Required: Prepare a direct materials purchases budget (in pounds) for April.