# Inequalities help

So I need help with setting up the equation to graph it (eg. y = mx + b) but with different variables.

In a factory, Machine A Produces 60 Cornflakes boxes per hour and Luckycharms at 70 boxes per hour. Machine B produces produces 40 cornflake boxes per hour and Luckycharms 40 per hour. It costs $50 a hour to run machine A and$30 a hour to run Machine B. Machine A cannot run more then 9 hours a day and Machine B cannot run more then 10 hours a day. Atleast 240 cornflakes boxes need to be made and 140 lucky charm boxes need to be made.

So, I setup my variables:

Cornflakes = C
Luckycharms = L

And here are my equations (there cannot be more than 4 constraints):

60C + 70L <= 9 (machine A)
40C + 20L <= 10 (machine b)
C >= 240
L >= 140

My equation is wrong though. If I solve and graph it (L = Y, C = X), it does not come out correctly.

Can someone help?

Related Precalculus Mathematics Homework Help News on Phys.org
jbunniii
Homework Helper
Gold Member
Your first two inequalities are wrong.

If C and L are the number of boxes of each type produced, then what is 60C? What is 70L? What are the units of these things? 60 = number of boxes per hour, C = number of boxes, so the units of 60C are (number of boxes)^2 / hour. This is not what you want.

Also, if C and L represent the TOTAL number of boxes of each type produced, then you seem to be assigning this total number to be produced by both machine A and machine B. Thus you will operate the machines longer than needed.

What if instead of C and L, you were to use two variables A and B, representing the number of hours of operation of machines A and B?

Then you would have these constraints:

\begin{align*} A &\leq 9 \\ B &\leq 10 \\ 60A + 40B &\geq 240 \\ 70A + 40B &\geq 140\end{align*}

This assumes that all the production has to take place in one day. Does it?

Also, what additional constraint do the operating costs impose? Is the goal to choose A and B to minimize the total cost? (I assume so.) Then you will have to express this cost in terms of A and B and work out how to minimize it.

Last edited:
yes, i need to find the most miminzied cost, so i would graph this.

jbunniii
Homework Helper
Gold Member
Sorry, my initial response assumed that each machine could produce box C *or* box L at a certain rate per hour, but on closer reading I believe you mean that each machine can produce *both* types simultaneously, at the stated rates. I've modified my original post accordingly. (You might need to hit "refresh" to see it.) Is that interpretation correct?

Sorry, my initial response assumed that each machine could produce box C *or* box L at a certain rate per hour, but on closer reading I believe you mean that each machine can produce *both* types simultaneously, at the stated rates. I've modified my original post accordingly. (You might need to hit "refresh" to see it.) Is that interpretation correct?

Oh i see now, yes it is. Thank you very much, I have a huge headache considering I've been working on this for 2 hours =/

Time for sleep and I will finish the rest of my assignment tomorrow. Thank you.

jbunniii
Homework Helper
Gold Member
Oh i see now, yes it is. Thank you very much, I have a huge headache considering I've been working on this for 2 hours =/

Time for sleep and I will finish the rest of my assignment tomorrow. Thank you.
No worries, and good luck.

By the way, if you really want to use C and L instead of A and B, you can certainly do so, by solving these equations for A and B:

\begin{align*}60A + 40B &= C \\ 70A + 40B &= L \end{align*}

Then the last two inequalities become

\begin{align*} C &\geq 240 \\ L &\geq 140 \end{align*}

and the first two inequalities end up looking pretty weird and unintuitive. I think it's more natural to use A and B as I defined them.