Question

a furniture shop refinishes cabinets. employees use one of two methods to refinish each cabinet. Method I takes 2 hour and materials cost $9. Method II takes 2.5/hrs and cost $5 in materials. next week, they plan to spend 219 hours in labor and $648 in materials. how many cabinets should they plan to refinish with each method?

Answer 1

First, I'd calculate how many cabinets they could do for each method in 219 hours:

Method 1:\[\frac{219}{2} = 109.5~cabinets\]Method 2:\[\frac{219}{2.5} = 87.6~cabinets\]
Now consider the material cost if all of those cabinets were made:

Method 1:\[109.5 * $9 = $985.50\]Method 2:\[87.6 * $5 = $438.00\]
Now figure what the limiting factors are:

Method 1 is limited by cost because building all the cabinets you can in 219 hours exceeds $648. Therefore, calculate how many cabinets can be built using that method with only $648:
\[\frac{$648}{$9}=72~cabinets\]Method 2 is limited by time because if you build all 87.6 cabinets in 219 hours you're still under $648. Therefore, you can only build 87.6 cabinets with method 2. That should round down to 87 since you can't see a partially finished cabinet.

Answer 2

*"see" should have been "sell" in the last sentence...typo.

Answer 3

Iappreciate the effort but it was incorrect. I have a different question now.....

Answer 4

I suppose I misunderstood the question then. I thought it was asking how many you could make using each method. It's apparently asking the best combination of both methods to make the most cabinets.

Let x = number of cabinets using method 1
Let y = number of cabinets using method 2

Then:
219 = 2x + 2.5y
648 = 9x + 5y

I assume that you know how to solve this system of equations for x and y. You should end up with making 42 cabinets using method 1 and 54 cabinets using method 2...for a total of 96 cabinets.