Description
The last question requires using MATLAB.
If graphs are asked need to be drew, you can use Desmos.com and then printed it out to annotate the corner points and stuff. (It's fine if you have other preferred ways to draw the graphs)
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Explanation & Answer
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Assignment
MATH 171 A: Linear Programming
Type University name here
Date: January 15, 2021
Submitted to: Prof. Philip E. Gill
Submitted by:
Exercise 1.1.
(a) Solution. The optimization problem for the JuiceCo mixture in mathematical form was
formulated in the class. The constraints for JuiceCo problem are given below:
3𝑥 + 2𝑦 ≤ 200
𝑥 + 2𝑦 ≤ 100
𝑥≥0
𝑦≥0
Here, x represents gallons of craneapple and y represents gallons of appleberry.
The graph for the above problem can be plotted in Matlab or on desmos with a little effort.
The graph drawn on desmos is shown below:
Figure 1.1: Graph for the optimization model with corner points
The gallons of each juice for corner points can be tabulated as follows:
Corner point
(0,0)
(0,50)
(50,25)
(200/3,0)
Gallons of cranapple
0
0
50
200/3
Gallons of appleberry
0
50
25
0
It is given that the profit is 𝑃 = 3𝑥 + 4𝑦
At (0,0), the profit is 𝑃 = 3 × 0 + 4 × 0 = 0
At (0,50), the profit is 𝑃 = 3 × 0 + 4 × 50 = 200
At (50,25), the profit is 𝑃 = 3 × 50 + 4 × 25 = 250
At (200/3,0), the profit is 𝑃 = 3 ×
200
3
+ 4 × 0 = 200
It’s observed that the profit is maximum at x =50 and y = 25 and the maximum profit is 250
(b)
(i) 𝑝𝑟𝑜𝑓𝑖𝑡 = 3𝑥 + 4𝑦
The maximum profit is for the corner point (50, 25) and the maximum profit is 250
(ii) 𝑝𝑟𝑜𝑓𝑖𝑡 = 2𝑥 + 5𝑦
Table for the profit can be given as follows
Corner points
Profit
(0, 0)
2×0+5×0=0
(0, 50)
2 × 0 + 5 × 50 = 250
(50, 25)
2 × 50 + 5 × 25 = 225
(200/3, 0)
2×
...