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.

Question

We have to figure out the choices that will optimize the profit and minimize her cost.

thank you for the help!!!

Answer 1

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.