Craftsmen install 500 sq ft of ceramic tile and 200 sq ft of vinyl tile in one day. An apprentice installs 100 sq ft of ceramic tile and 200 sq ft of vinyl tile in one day. The firm has a job that requires 2400 sq ft if ceramic tile and 1600 sq ft of vinyl tile. Tessa pays craftsmen $200 per day and apprentices $120 per day.
We have to figure out the choices that will optimize the profit and minimize her cost.
thank you for the help!!!
Cost of ceramic tile laying
Craftsman: 500/200 or 2.5 tiles/dollar
Apprentice: 100/120 or .85 tiles/dollar.
Cost of Vinyl:
Craftsman: 200/200= 1 tile/dollar
Apprentice: 200/120= 1.66 tiles/dollar
So looking at productivity, Craftsman can lay ceramic tile well, and apprentice can do the leftover vinyl
I wonder if you really mean AND in the data, or meant OR
If you really meant AND, then start here:
1) Hire 5 craftsman: They lay 2400 ceramic tile AND 1000 sq ft of Vinyl.
Hire three apprentices, they lay 600 square feet of vinyl
Cost of this option: 5*200 + 3*120=1360
Compare this option to ...
2) hire 4 craftmen to do 2000 ft^2 of ceramic tile, and 800 sqft of vinyl
and hire 4 apprentice to do 400 sqft of ceramic, and 800 sqft of vinyl
Cost of this option is 4*200 + 4*120= 1280
compare this option to
2) Hire 3 craftsmen to do 1500 sqft ceramic and 600 vinyl, and
Hire 10 apprentices to do 900 sqft of ceramic tile and 1000 sqft of vinyl
Cost= 3*200 + 10*120= 1800 dollars.
It pays to use the most productive folks, option 2
If you meant lays 500 sqft ceramic OR 200 sqft vinyl, that is a different solution.
To optimize profit and minimize cost, we need to determine the number of craftsmen and apprentices to hire in order to complete the job efficiently. Let's break down the problem and calculate the various costs involved.
Let's represent the number of craftsmen as C and the number of apprentices as A. We know that craftsmen install 500 sq ft of ceramic tile and 200 sq ft of vinyl tile in one day, while apprentices install 100 sq ft of ceramic tile and 200 sq ft of vinyl tile in one day.
To complete the job, we need to install 2400 sq ft of ceramic tile and 1600 sq ft of vinyl tile. We can set up the following equations based on the installation rates:
500C + 100A = 2400 (for the ceramic tile)
200C + 200A = 1600 (for the vinyl tile)
Now, we can solve these equations to determine the number of craftsmen and apprentices required:
From the first equation:
500C + 100A = 2400
5C + A = 24
From the second equation:
200C + 200A = 1600
C + A = 8
Now we have a system of two equations:
5C + A = 24
C + A = 8
We can solve this system using substitution or elimination method. Let's use the elimination method to find the values of C and A:
(5C + A) - (C + A) = 24 - 8
4C = 16
C = 4
Now, substitute the value of C into one of the equations:
C + A = 8
4 + A = 8
A = 4
So, to complete the job efficiently, Tessa should hire 4 craftsmen and 4 apprentices.
Next, let's calculate the costs involved:
The craftsmen cost per day is $200, and the apprentices cost per day is $120. Since there are 4 craftsmen and 4 apprentices, the total daily cost would be:
Total cost = (Craftsmen cost per day x Number of craftsmen) + (Apprentices cost per day x Number of apprentices)
= ($200 x 4) + ($120 x 4)
= $800 + $480
= $1280
Therefore, the daily cost for Tessa to complete the job efficiently would be $1280.
To optimize profit, Tessa needs to consider the amount she will charge for the job. Once we know the revenue, we can subtract the cost to determine the profit. This information is required to make a decision on how to optimize the profit and minimize the cost.
I hope this helps!