Formulate an optimization model (decision variables, objective function, and constraints) to help the company identify the optimal production plan. b) Solve the model using Lingo/Excel and explain the results obtained in the booklet
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A clothing company produces three types of sport jackets (types 1, 2, and 3), each with different resource
requirements (hours of labor, units of leather, and units of wool) (see the table below). The unit costs of
these resources are $5 per hour of labor, $7 per unit of leather, and $3 per unit of wool. In each production
cycle, the company has 1000 hours of labor available, 800 units of leather, and 900 units of wool.
To avoid inventory at the end of the production cycle, the sales department has set maximum production
limits for each jacket type (i.e., no more than that should be produced): 200 jackets of type 1, 100 jackets
of type 2, and 150 jackets of type 3. The company wants to determine the optimal production plan for the next production cycle that maximizes total profit, subject to the resource availability and production limits.
Type 1 | Type 2 | Type 3 | |
Labor time required (hours) | 3 | 2 | 2 |
Leather (units) | 3 | 2 | 0.5 |
Wool (units) | 0.5 | 2 | 3 |
Sale price ($/jacket) | $50 | $38 | $29 |
a) Formulate an optimization model (decision variables, objective function, and
constraints) to help the company identify the optimal production plan.
b) Solve the model using Lingo/Excel and explain the results obtained in the booklet
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- Because of its labor contract, a company must hire enough labor for 100 units ofproduction per week on one shift or 200 units per week on two shifts. It cannot hire,lay off, or assign overtime. During the fourth week, workers will be available fromanother department to work part or all of an extra shift (up to 100 units). There is aplanned shutdown for maintenance in the second week, which will cut production tohalf. Develop a production plan. The opening inventory is 200 units, and the desiredending inventory is 300 unitsManufacturers Inc. (MI) currently has a labor force of 10, which can produce 600 units per period. The labor cost is now $5000 per period per employee. The company has a long-standing rule that does not allow it to make use of any overtime. In addition, the product cannot be subcontracted, due to the specialized nature of the machinery that MI uses to produce it. As a result, MI can only increase/decrease production by hiring or laying off employees. The cost is $10000 to hire or lay off an employee. Inventory carrying costs are $200 per unit for any unsold items at the end of the period. The inventory level at the beginning of period 1 is 400 units. The forecast demand is 700 in period 1,600 in period 2,450 in period 3, 250 in period 4,500 in period 5, and 550 in period 6. a.) Compute the costs of the Chase Demand Strategy. b.) Compute the costs of the Level Strategy c.) Compare the costs of the two strategies. Which one is superior?A diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units of Vit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.
- The textile company “Designs Sports” is dedicated to the production of sports clothing. In its line has shorts, pants and t-shirts. From management they requested to manufacture the quantity of each product to maximize profits. To manufacture each type of garment It goes through two areas, sewing and finishing. Furthermore, all three garments require the same type of fabric. Two people work in the sewing area, while in the production area finished only one. In the company we work 8 hours a day, 5 days a week. The Weekly fabric availability is 375 square meters. Lastly, each shirt contributes $100 US to profits, each short with $80 US; and each pair of pants with $150 US. Solve this operations research problem.Manufacturing Aggregate Planning Manufacturers Inc. (MI) currently has a labor force of 10, which can produce 600 units per period. The labor cost is now $5000 per period per employee. The company has a long-standing rule that does not allow it to make use of any overtime. In addition, the product cannot be subcontracted, due to the specialized nature of the machinery that MI uses to produce it. As a result, MI can only increase/decrease production by hiring or laying off employees. The cost is $10000 to hire or lay off an employee. Inventory carrying costs are $200 per unit for any unsold items at the end of the period. The inventory level at the beginning of period 1 is 400 units. The forecast demand is 700 in period 1,600 in period 2,450 in period 3, 250 in period 4,500 in period 5, and 550 in period 6. a.) Compute the costs of the Chase Demand Strategy. b.) Compute the costs of the Level Strategy c.) Compare the costs of the two strategies. Which one is superior?A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Maximum Labor-Hours Department Fabricating Finishing Trick Ski Slalom Ski Available per Day 9. 432 63 If the profit on a trick ski is $30 and the profit on a slalom ski is $50, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ The maximum occurs when trick skis and slalom skis are produced.
- A company plans to produce 25,000 units in a 3-month period. The months have 22, 21, and 20 working days, respectively. What should the average daily production be?Formtech Inc. produces transformers. Each order is custom designed and manufactured for the customer. Each order goes through 3 phases: Transformer Design, which takes 4 weeks. Procurement, which has a lead time of 8 weeks. Assembly and Testing, which takes 4 weeks The design group can handle only 4 projects at any given time. The other groups are not capacity constrained. How much total work-in-process (number of projects started but not yet completed) does the company typically have? (Hint: Little's Law)The senior management at Davis Watercraft would like to determine if it is possible to improve firm profitability by changing their existing product mix. Currently, the product mix is delermined by giving resource priority to the highest contribution margin watercrafts. Davis Watercraft always has a contingent of 10 workers on hand; each worker is paid $25 per hour. Overhead costs are $38,000 per week. The plant operates 18 hours per day and 6 days per week. Labor is considered a fixed expense because workers are paid for their time regardless of their utilization. The production manager has delermined that workstation 1 is the bottleneck. Delailed production information is provided below. Model A B Price $495 $345 $525 Material costs $45 $35 $115 Weekly demand Processing Time Station 1 Processing Time Station 2 Processing Time Station 3 Processing Time Station 4 100 75 40 60 30 60 10 60 20 30 40 a. Using the traditional method, which bases decisions solely on a product's contribution…
- 4. The Spencer Optics Company produces an inexpensive line of sunglasses. The manufacturing process consists of assembling two plastic lenses (produced by the firm's plastic molding depart- ment) into a finished frame (purchased from an outside supplier). The company is interested in using material requirements planning to schedule its operations and has asked you to prepare an example to illustrate the technique. The firm's sales manager has prepared a 10-week sales forecast for one of the more popular sunglasses (the Classic model) for your example. The forecast is 100 units per week. Spencer has customer orders of 110 units, 80 units, 50 units, and 20 units in weeks 1, 2, 3, and 4, respectively. The sunglasses are assembled in batches of 300 units. Presently, three such batches are sched- uled: one in week 2, one in week 5, and one in week 8. Complete the following time-phased record: Week hand 1 2 3 4 5 6 7 8 9 10 Classic Model On MPS Record Forecast Orders Projected available…A company produces two products: A and B. Prod-uct A sells for $11 per unit and product B sells for $23 per unit. Producing a unit of product A requires two hours on assembly line 1 and one unit of raw ma-terial. Producing a unit of product B requires two units of raw material, one unit of A, and two hours on as-sembly line 2. On line 1, 1300 hours of time are avail-able, and 500 hours are available on line 2. A unit of raw material can be bought (for $5 a unit) or produced(at no cost) by using two hours of time on line 1.a. Determine how to maximize profit.b. The company will stop buying raw material whenthe price of raw material exceeds what value? (UseSolverTable.)LBC Corporation makes and sells a product called Product WZ. Each unit of Product WZ requires 3.0 hours of direct labor at the rate of $26.00 per direct labor-hour. Management would like you to prepare a Direct Labor Budget for June. The budgeted direct labor cost per unit of Product WZ would be: $78.00 $7.00 $26.00 $46.00