A linear programming computer package is needed.Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be made next month.Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.Manufacturing CostComponentFrameMinSupportStrapComponentFrameSupportStrapCutting constraintThree departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.Milling constraintShaping constraintFrame constraintSupport constraint$37.00Strap constraint$10.50$5.50(FM, FP, SM, SP, TM, TP) =3.51.30.8DepartmentCutting Milling Shaping350Purchase Cost2.2Capacity (hours)(a) Formulate and solve a linear programming model for this make-or-buy application. (Let FM = number of frames manufactured, FP = number of frames purchased, SM = number of supports manufactured, SP = number of supports purchased, TM = number of straps manufactured, and TP = number of straps purchased. Express timein minutes per unit.)1.7$50.00$14.00420$6.503.12.61.7680FM, FP, SM, SP, TM, TP 20How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number.)(b) What is the total cost (in $) of the manufacturing and purchasing plan?(c) How many hours of production time are used in each department? (Round your answers to two decimal places.)CuttinghrsMillinghrsShapinghrs

Decision Variables: Suppose-FM be the no. of frames manufacturedFP be the no. of frames…

A linear programming computer package is needed. Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Manufacturing Cost Purchase Cost Frame Support Min Strap Component Frame Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. Department Cutting Milling Shaping 3.5 2.2 3.1 Support Strap Capacity (hours) Cutting constraint Milling constraint Shaping constraint Frame constraint Support constraint $37.00 Strap constraint $10.50 $5.50 1.3 hrs hrs hrs 0.8 (a) Formulate and solve a linear programming model for this make-or-buy application. (Let FM-number of frames manufactured, FP number of frames purchased, SM number of supports manufactured, SP number of supports purchased, TM-number of straps manufactured, and TP-number of straps purchased. Express time in minutes per unit.) 350 1.7 $50.00 $14.00 $6.50 420 2.6 1.7 680 FM, FP, SM, SP, TM, TP 20 How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number) (FM, FP, SM, SP, TM, TP) ( (b) What is the total cost (in $) of the manufacturing and purchasing plan? $ (c) How many hours of production time are used in each department? (Round your answers to two decimal places.) Cutting Milling Shaping

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P