Question

Problem 3-25 Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 50 42 30 Hours required to complete all the oak cabinets 60 48 35 Hours required to complete all the cherry cabinets Hours available 40 30 35 Cost per hour $36 $42 $55 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. a. Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. Let 0 1 = percentage of Oak cabinets assigned to cabinetmaker 1 0 2 = percentage of Oak cabinets assigned to cabinetmaker 2

Answer 1

According to date : P.Nol a OI 02 03 с Ci ca C3 min 1800 1764 1650 3160 2016 1925 Sot O, 02 03 С. C2 C3 Hours I 50 0 0 6010 40 Hours a 42 48 30 Hours 3 O 35 30 o 35 oak 1 Cherry 1 1 1 01, 02, 03, C1, C2,C320 Cabinetmaked Cabinet maker a Cabinetmaker 1 3 Oak 0.27 0.000 0.729 cherry 0.000 0.625 0.345 Total Cost 3,673

P. 2 c) no, slack, 26.458,0,0 or) yes, -1.75, 1.75, 41.143 Cabinet maker I Cabinet maker a Cabinetmaker 3 Oak 0.271 0.000 0.729 cherry 0.000 0.625 0.375 total Cost 3553 =) The change in Cabinetmaker als Cost per hour leade to changing (9) objective function Coefficients. This means that the liner Program (freed to be reteron) » The new optional solution is (is the same as) above but with a total Cost of $ 3,553 a please give me positive like. It's help a lot anel any queries Comment below. Tq4... me