SOLUTION: ronald needs to earn at least Php 2,500 from his two jobs to cover his weekly expenses. this week, he can work for at 42 hours. his job as a gas station attendant pays php 52.50 pe

Question 1093389: ronald needs to earn at least Php 2,500 from his two jobs to cover his weekly expenses. this week, he can work for at 42 hours. his job as a gas station attendant pays php 52.50 per hour while his job as parking attendant pays php 40 per hour.
A. write a system of linear inequalities to model the given situation?
B given this conditions, can ronald be able to meet his target of earning php 2,500? why or why not? justify your answer.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
he needs to earn at least 2500 php.
he can work as much as 42 hours this week.
he can earn 52.50 per hour working as a gas attendant.
he can earn 40 per hour working as as a parking attendant.

if he could work all the 42 hours as a gas attendant, he will earn 42 * 52.50 = 2205 php.

therefore, he won't make enough money to cover his expenses if he can only work 42 hours a week.

let x = the number of hours working as a gas attendant.
let y = the number of hours working as a parking attendant.

if you look at this as a system of linear inequalities type problem then you can do the following:

your objective function is r = 52.50 * x + 40 * y

this is what you want to maximize.

your constraints are:

x >= 0
y >= 0
x + y <= 42

if you graph these constraints, then the feasible region is the area of the graph that is not shaded.

the corner points of that feasible region are (42,0) and (0,42) and (0,0).

(0,0) is irrelevant and therefore excluded from consideration in this problem.

you evaluate the objective function at these corner points to get:

at (42,0), 52.50 * 42 + 40 * 0 = 2205
at (0,42), 42.50 * 0 + 40 * 42 = 1680

his maximum revenue is when he works all 42 hours as a gas attendant.

unfortunately, this isn't enough to cover his expenses.

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