The firm
manufactures two models of the trans catheter aortic valve replacement system:
the system...

Question

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 of23
mm valvesper week and no more than 600 units of 29 mm valves per week.

The
manufacturing time for one23 mm aortic valvesystemis 2 hours per week. The
manufacturing time for one29 mm aortic valve system is 2.4 hours per week. There are 1550 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.

David · Accepted Answer

Discussion question
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 of23 mm valvesper week and no more than 600 units of 29 mm valves per week.
The manufacturing time for one23 mm aortic valvesystemis 2 hours per week. The manufacturing time for one29 mm aortic valve system is 2.4 hours per week. There are 1550 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.
Solution:
Given data from the problem:
The two types of the valves are 23 mm valve and 29mm valves
The possible profit from 23 mm valve is $300 per unit.
The possible profit from 29 mm valve is $360 per unit.
Suppose A be the number of valves of 23 mm size and B be the number  of valves of 29mm size possible to manufacturer for a week,  then the possible profit from the sale  of the valves will be,
Objective function:
Z = 300A + 360B ------------- (Maximize)
Constraints:
A= 0 
Solution:
Problem is 
	Max Z
	=
		300
	x1
	+
	360
	x2
	
	subject to
	2
x1
+
2.4
x2
≤
1550
x1
≤
300
x2
≤
600
	and x1,x2≥0;
The problem is converted to canonical form by adding slack,

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...

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