AaBbCel Aatbcat Aatbcet AaBb Authce Heading 2 Normal 1 No Spac. Styles Hint: Uti

Question

AaBbCel Aatbcat Aatbcet AaBb Authce Heading 2 Normal 1 No Spac. Styles Hint: Utilize queuing theory 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 systen which is equipped with 23 mm valves and the systerm 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. 1o

Explanation / Answer

Let the units of 23 mm valve be x and 29 mm valve be Y

Given conditions are X < 300, Y< 600

profit function: 300 x + 360 Y

1.6 x + 1.8 Y < 1520

From the above Conditions we get the values of X, Y as (275,600) Since y product yield a profit of 360 compared to x 300

275 (1.6)+600(1.8)= 440+1080 = 1520

Maximum profit it yields P= 300×275+ 360×600 = 82,500+216,000 = 298,500

The manager should manufacture 275 units of 23 mm valve and 600 units of 29 mm valve

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