Graphs and Relations Question

[albert]

I was wondering if anyone could help me out with this question

A taxi is repaired and serviced at Joe's garage which specialises in repairs. Brake repairs generally require three hours of qualified labour and two hours of apprentice labour with a profit of $75 per job. Clutch repairs generally takes three hours of qualified labour and four hours of apprentice labour with a profit of $120 per job.

The company employs three qualified mechanics and three apprentice mechanics. All employees may work a maximum of 38 hours per week.

Let b represent the number of brake repairs per week and c represent the number of clutch repairs per week.

a.) state the four inequations of the constraints.

I know this is probably an easy question but i can't seem to work it out

[Stick]

Finding constraints from a worded problem takes a bit of practice initially, but they jump out at you after a while. That being said, you need to read this particular question a few times in order to find them! Let me help you out.

The first inequality refers to the amount of qualified labour is possible throughout the week: 3b+3c≤114 (it is 114 and not 38 because there are three workers, not one. It is also not necessary to simplify the inequalities unless the question states to do so)

The second inequality refers to the amount of apprentice labour is possible throughout the week: 2b+4c≤114

I think the third and fourth inequalities are just b≥0 and c≥0 (you cannot have a negative amount of repairs), because I have used up all the relevant information coming up with the first two constraints. Ignore the profit information because that will be used to find the profit objective function found later in the problem.

This question was quite challenging so if you don't mind I'd like you to verify my answers with the suggested solution (I'd also be interested to see the solutions myself, if they are in fact different).