consider the following linear programming problem
Z max : 6X1 + 5X2
Subject to
X1 + X2 5
3X1 + 2X2 12
X1, X2 >0
A. Solve the above LLP by using graphical solution( put each steps)
Answers
Answer:
We wish to maximize the number of sandwiches, so let:
x = # of ham sandwiches
y = # of light ham sandwiches
z = # of vegetarian sandwiches
The total number of sandwiches is given by
S = x + y + z
The constraints will be given by considering the total amount of ingredients available. That is, the company has a limited amount of ham, vegetables, cheese, and bread.
In total, the company has
10(40) = 400 slices of ham, 18(14) = 252 slices of bread, 200 servings of vegetables, and 15(60) = 900 slices of cheese available. At most, the company can use the above amounts.
There are two sandwiches that use ham—the first requires 4 slices of ham and the second requires only 2, per sandwich. That is, 4x + 2y ≤ 400
That is, the total number of slices of ham cannot exceed 400.
Each sandwich requires 2 slices of bread so 2x + 2y + 2z ≤ 252
The ham sandwiches have 1 and 2 servings of vegetables, respectively, and the vegetarian sandwich has 3 servings of vegetables. So, 1x + 2y + 3z ≤ 200
Both ham sandwiches require one slice of cheese, and the vegetarian sandwich requires two slices of cheese, so, 1x + 1y + 2z ≤ 900 Below is the completed linear programming model for this example.
