Question

Problem 4 As Operations Manager, you would like to know which product mix needs to be manufactured. The firm manufactures two models of the trans catheter aortic valve replacement system: the system which is equipped with 23 mm valves and the system which is equipped 29 mm valves. The expected profit for 23mm system is $300 per unit, while profit for 29mm system is $360 per unit. The firm utilizes aortic valves bought from an external supplier. There is a supply restriction for both of 23 mm and 29mm valves. The current suppler of valves cannot supply more than 300 units of 23 mm valves per week and no more than 600 units of 29 mm valves per week. The manufacturing time for one 23 mm aortic valve system is 1.6 hours per week. The manufacturing time for one 29 mm aortic valve system is 1.8 hours per week. There are 1520 hours of total manufacturing time available per week. Determine how many units of 23 mm aortic valve system and 29 mm aortic valve system the firm needs to manufacture per week to maximize profit. Hint: Set up and solve the problem as Linear or Integer Programming problem using Excel QM, POM, or Solver.

Answer 1

A C D Decision Variables 1 Number of units of each type of valve to be made 2 23 mm valve 29mm valve 3 4 No.of units Objective function 5 Maximize the profit 6 7 EB4*300+C4*360 Constraints 8 9 B4 300 <= 10C4 600 11-1.6*B4+1.8*C4 1520 12 13

A B C Decision Variables 1 Number of units of each type of valve to be made 23 mm valve 29mm valve 2 3 4 No.of units Objective function 5 Maximize the profit 6 7 Constraints 8 0 300 10 0 600 11 0 1520 12 LL LC

Solver Parameters X eet SAS7 Set Objective: To: O Value Of: 0 Min Max By Changing Variable Cells: SB$4:SC$4 Subject to the Constraints: SAS9:SAS11 SBS4:SC$4 >= 0 SCS9:SCS11 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth Help Solve Close

A C Decision Variables 1 Number of units of each type of valve to be made 23 mm valve 29mm valve 3 4 No.of units 275 600 Objective function 5 Maximize the profit 6 7 298500 Constraints 275 300 10 600 600 11 1520 1520 12 13 LC