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Production mix problem help

Asked by Suman Koirala on 23 Apr 2013
Quiz 9: Calculation of Production Mix 
Hours 
Reactor A 
Reactor B 
Product 1 
5 
3 
Product 2 
3 
3 
Product 3 
3 
4 
The table shows how many hours it takes reactors A and B to produce a ton of each 
product. From the table we see that for every ton of product 1 produced we need to 
run Reactor A for 5 hours and also run Reactor B for 3 hours. The two reactors are 
available for 40 hours and 30 hours per week respectively. We can determine the 
amount (in tons) of product 1, p 1 , product 2, p 2 , and product 3, p 3 that can be 
produced in a week using the following equations: 
5 p 1 + 3 p 2 + 3 p 3 = 40 
3 p 1 + 3 p 2 + 4 p 3 = 30 
Let F 1 , F 2 , F 3 represent the profit for a ton of each product . So the total weekly 
profit is given by: 
Profit = F 1 p 1 + F 2 p 2 + F 3 p 3 
Create a script M-file that uses the reduced row echelon function rref to solve for p 1 
and p 2 as functions of p 3 , and generates two subplots. The first subplot should show 
the total weekly profit as a function of p 3 for the following two cases: 
Case 1: F 1 = $400, F 2 = $600, F 3 = $100 
Case 2: F 1 = $600, F 2 = $200, F 3 = $200 
The second subplot shows p 1 and p 2 as a function of p 3 . 
Based on the results of the first subplot, your production manager says that she is 
going to adopt an all or nothing strategy on the production volume of product 3. She 
says that the plant will either produce the maximum amount of product 3 or none at 
all. What is her justification for this? 

This is what I have so far. My second subplot looks wierd.

A=[5 3; 3 3];
b=[40- 3*p3; 30-4*p3];
p=A\b;
f1=400; f2=600; f3=100;
p3=[0:0.1:40];
P=f1*p(1)+f2*p(2)+f3*p3;
subplot(1,2,1)
plot(p3, P)
hold on
f1=600; f2=200; f3=200;
P=f1*p(1)+f2*p(2)+f3*p3;
plot(p3, P)
subplot(1,2,2)
plot(p(1),p3)
hold on
plot(p(2),p3)

Any suggestion is appreciated. Thanks!

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Suman Koirala

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