## Production mix problem help

### Suman Koirala (view profile)

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!

## Products

No products are associated with this question.

#### Join the 15-year community celebration.

Play games and win prizes!

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi