Linear Optimization
It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.
We'll use the graphic method to solve the problem.
The problem is as follows:
Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.
The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:
x + y ≤ 130 (1)
She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:
3.75x + 6y ≥ 600
Multiply this inequality by 4:
15x + 24y ≥ 2400
And divide it by 3:
5x + 8y ≥ 800 (2)
We are given a final condition that she can sell a minimum of 80 burritos, thus:
y ≥ 80 (3)
There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:
x ≥ 0 (4)
y ≥ 0 (5)
Let's put this all together:
x + y ≤ 130 (1)
5x + 8y ≥ 800 (2)
y ≥ 80 (3)
x ≥ 0 (4)
y ≥ 0 (5)
The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).
We need to graph all five lines in one common grid. It's shown below.
According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos