The Trim-Look Company makes several lines of skirts, dresses, and sport coats. Recently, a consultant suggested that the company reevaluate its South Islander line and allocate itsresources to products that would maximize contribution to profits and to overhead. Each product requires the same polyester fabric and must pass through the cutting and sewingdepartments. The following data were collected for the study.a. Let X₁ = number of skirts produced,X₂ = number of dresses produced,X3 = number of sport coats produced.ProductSpecify the objective function and constraints for the problem.Objective function: Maximize Z = X₁ + x₂ + x3SkirtDressSport coatProcessing Time (hr)CuttingSewing213325Material (yd)The cutting department has 120 hours of capacity, sewing has 200 hours of capacity, and 120 yards of material are available. Each skirt contributes $9 to profits and overhead;each dress, $21; and each sport coat, $35.15

Linear programming (LP) is a mathematical optimization technique that helps solve problems where an…

Answered: a. Let X₁ = number of skirts produced,…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A manufacturing fi rm has discontinued production of a certain unprofi table product line.Considerable excess production capacity was created as a result. Management is consideringdevoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit areProductMachine Type X1 X2 X3Milling machine 8 2 3Lathe 4 3 0Grinder 2 0 1The available time in machine hours per week isMachine Hours per WeekMilling machines 800Lathes 480Grinders 320The salespeople estimate they can sell all the units of X1 and X2 that can be made. Butthe sales potential of X3 is 80 units per week maximum.Unit profi ts for the three products areUnit ProfitsX1 $20X2 6X3 8a. Set up the equations that can be solved to maximize the profi t per week.b. Solve these equations using the Excel Solver.c. What is the optimal solution? How many of each product should be made, and whatshould the resultant profi t be?d. What is this situation with respect to the machine groups? Would they…
The manager of Jokitian Iron Works Company received an order to produce anumber of pipes which require the use of material A costing $3 and material Bcosting $8 per unit. For each pipe no more than 12 units of Material A and at least16 units of material B must be used. While each unit of A weighs 4 pounds andeach unit of B weighs 6 pounds, the final product must weigh exactly 120 pounds.a. Present the objective function.b. Present the constraint functions.c. Show and label the graph of the feasible solution.d. How many units of each raw material should be used in order to producethe ordered pipes most economically?e. What is the cost of each pipe?
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a. Let X₁ = number of skirts produced, X₂ = number of dresses produced, X3 = number of sport coats produced. Specify the objective function and constraints for the problem. Objective function: Maximize Z = X₁ + x₂ + x3