I'm stuck on this linear inequality. it says:

A furniture company makes 2 table legs; one plain and one fancy. The plain legs take 2 hrs on a lathe and 1 hour sanding to make. The Fancy legs take 1 hour on a lathe and 4 hrs sanding to make. the warehouse has 4 lathes and 6 sanding machines, which are available 12 hrs per day. Each plain leg nets $3 in profit and each fancy legs nets $5. how can the company maximize profit?

I was told this could be done with calculus, but how can it be done with algebra?

Question

I'm stuck on this linear inequality. it says:

A furniture company makes 2 table legs; one plain and one fancy. The plain legs take 2 hrs on a lathe and 1 hour sanding to make. The Fancy legs take 1 hour on a lathe and 4 hrs sanding to make. the warehouse has 4 lathes and 6 sanding machines, which are available 12 hrs per day. Each plain leg nets $3 in profit and each fancy legs nets $5. how can the company maximize profit?

I was told this could be done with calculus, but how can it be done with algebra?

anonymous · Answer

How is this done in calculus when the question is so long winded?

anonymous · Answer

Dunno, I don't know calculus. This was a question in a college algebra book, which is what I'm trying to learn.

anonymous · Answer

This question should be done in algebra

anonymous · Answer

The Chapter is about linear inequalities and linear programming

anonymous · Answer

It would definitely help me if someone could answer it using algebraic principles since I don't know calculus

anonymous · Answer

The terms to list in linear programming
P=Plain, F = Fancy, H = hours
P= 1S+2L of (manhours) = total is 3h
F= 4S+1L of (manhourse) = total is 5h
Available resources: 4L+6S = 12h
Plain profit = $3/leg
Fancy profit = $5/leg

anonymous · Answer

Using algebra we can solve for max profit=
Try to equate the available resources to P & F's profit. At same time include their production per leg per manhour