need help answering this question:

Question

A small industry produces two items, 1 and 2. It operated at capacity and makes a profit of $6 on each item 1 and $4 on each item 2. The following table gives the hours required to produce each item and the hours available per day.

item 1 item 2 hours available

assembly 2hrs 1hr 100

packaging 1hr 1hr 60

what is the number of items that should be produced each day to maximize profits? what is the maximum daily profit?

Answer 1

Meredith,

This question is probably a bit simpler than you think. But first, let's look at the trick of this problem!

Even though product 1 makes a profit of $6 and product 2 makes a profit of $4, both products are actually equally profitable!

Product 1 takes 3 hours to assemble and package: If we divide the $6 profit by those 3 hours, we realize that we are making $2 of profit per hour here.

Product 2 takes only 2 hours to assemble and package: If we divide the $4 profit by those 2 hours, we realize that we are making $2 of profit per hour here too.

So now, the profits don't even matter in this problem! All that matters is very simple algebra.

Look back at how long it takes to assemble each product and how many assembly hours we have total. Say that product 1 is x and product 2 is y. Rewrite the situation as 2x + y = 100. (It's 2x because product 1 takes 2 hours to assemble!)

Now look at how we have 60 hours to package and how each product takes the same 1 hour to package. Write this situation as x + y = 60.

I don't really want to walk you through basic algebra considering that you are already in an Economics class, but here we go:

Use the second equation to realize that x = 60 - y.

Plug this value in for x in the first equation, so that we have 2(60 - y) + y = 100.

120 - y = 100.

y = 20.

Clearly this means that x = 40.

I trust you can figure out the max profit from here.

Hope this helps. :)