Question

You are currently working two jobs so that you can earn enough money to go to the beach for Spring Break Pollo Tropical

(x) and Jason's Deli (4). Pollo Tropical pays $8/hour and requires that you work at least 10 hours/week. Jason's Deli pays
$8.75/hour but does not allow students to work more than 20 hours per week. Due to commitments, at school, you can't
work more than 28 hours/week. Write the objective function and a system of inequalities to model this situation.

Answer 1

First, let's define two variables:

x = number of hours that you work at the Pollo Tropical per week

y = number of hours that you work at Jason's Deli per week

Now, you want to get enough money to go to Spring Break, we do not know how much money we need for this, so let's suppose that you need M.

With the given information, we know that the weekly earnings are:

x*$8 + y*$8.75

We can define this as the objetive function, the one that says how much money you get as a function of x and y:

M(x, y) = x*$8 + y*$8.75

Now, we know that:

"Pollo Tropical requires that you work at least 10 hours per week"

Then:

x ≥ 10

"Jason's Deli does not allow students to work more than 20 hours per week."

y ≤ 20

"you can't work more than 28 hours/week."

x + y ≤ 28

Then we have:

M(x, y) = x*$8 + y*$8.75

And the system of inequalities is:

x ≥ 10

y ≤ 20

x + y ≤ 28