Optimizations Technique

[371204561]

Some students want to start a business that cleans and polishes cars. It takes 1.5 hours of labor and cost $ 2.25 in supplies to clean a car. It takes 2 hours of labor and cost $1,5 in supplies to polish a car. The students can work a total of 120 hours 1 week. They also decide that they want to spend more than $135 per week on supplies. The students expect to make a profit of $7.75 for each car that they clean and a profit of $8.50 for each car that they polish. What is the maximum profit the students can make?

[riptide]

Is this homework, you really should be doing it yourself

[woofgang]

not as much as if they did their own homeowrk and got better jobs

[fiction-factory]

>"They also decide that they want to spend more than $135 per week on supplies"
Should that say "no more than" rather than "more than"?

[bookbinder]

How much will they charge to clean a car, and to polish a car?

[fiction-factory]

i'm not sure we need to know that bookbinder as it's not just a profit /loss calculation that's needed.
I recall from memory that you can plot lines on a set of axis and use inequality regions. For example if work x hours on cleaning and y hours on polishing than x+y=120. And there will be others linking supply costs and a profit equation. If I had pen and paper i'd have a go.
I'd want to check the question is exactly right first - eg see my query re supply maximum spend, and also do we know the hourly wage rates (perhaps not)

[fiction-factory]

Probably easier to consider position if clean C cars and polish P cars
So we want to maximise profit of 7.75C+ 8.5P
This requires weekly hours of 1.5C + 2P = 120
We also know materials cost is 2.25C+1.5P and this is either more than, equal to or less than £135 (we need OP to clarify)

[TonyV]

More homework? You will learn more from doing it yourself from your course work and text books.

[drmorgans]

Yes, but it's fun to go back to O-levels maths once in a while. I guess $565 but I have craftily arched my hand so no-one can see the workings.

[fiction-factory]

Well I got $545 having arrived at 44 cleans and 24 polishes but I used a piece of paper the size of a small post it note and assumed they spent the full $135 on supplies

[fiction-factory]

If I get chance I'll look again later. Maybe the assumed constraint of spending $135 on supplies is wrong- maybe that is a minimum figure after all- so will explore that

[drmorgans]

I got 40 cleans and 30 polishes but my method wouldn't have convinced Miss Patton

[fiction-factory]

in my head yours works out okay and is better than mine, drM

[fiction-factory]

Yes,
1.5C+2P=120
2.25C+1.5P=135

so
4.5C +6P=360
9C+6P=540

Take one from t'other
4.5C=180 so C= 40
So P=30

[allenlondon]

Ask your President... he knows EVERYTHING.

[fiction-factory]

Of course all this depends on whether we have correctly interpreted what looks like a typo by the OP. We have assumed that he/she meant "spend NO more than $135 on supplies". If the OP's original wording is correct then the answer would be 80 cleans and 0 polishes which would give a profit of $620 (after a materials cost of $180 which is indeed more than $135 which is what the OP stipulated).
If the constraint should have said "no more than $135" though it seems an odd/short-sighted constraint as it means that they are missing out on the chance of a potentially larger profit.

[douglas9401]

Buff.

[fiction-factory]

Talking about yourself, douglas?
From my dictionary: (of a person or their body) in good physical shape with well-developed muscles.

[fiction-factory]

I think the OP may have forgotten which site she posted this query on or may not have worked out how to reply to her own question, so we may get no feedback

[fiction-factory]

Looks like 371204561 has forgotten about this. Still, it passed 15 minutes of lockdown time.
I suggest the students consider adding a 'Covid deep clean' option. Or apply for UC if they have to close, as they don't qualify for the Chancellor's support scheme for small businesses or furloughed workers

[fiction-factory]

Hi- I see you have been looking in today
Last Activity: 11:48 Thu 09th Apr 2020
Did drmorgans's solution help?