1. ## linear programming

'A clothier makes coats and salcks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coats requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 yards of wool and 4 hours of labor. The profit for a coat is $50 and the profit for slacks is$40. the clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.'

from the above question,i do not know how to determine the available amount of the two resources-square yards of wool and hours of labors

2. Originally Posted by Eyra
'A clothier makes coats and salcks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coats requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 yards of wool and 4 hours of labor. The profit for a coat is $50 and the profit for slacks is$40. the clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.'

from the above question,i do not know how to determine the available amount of the two resources-square yards of wool and hours of labors
Let c = #coats to be produced

Let s = #slacks to be produced

Our first constraint deals with square yards of wool. We cannot exceed 150 square yards. Using the fact that coats require 3 sq yds and slacks require 5 sq yds, we can identify this constraint.

$\displaystyle \boxed{3c+5s \leq 150}$

Our second constraint deals with the number of hours available being 200. Coats require 10 hrs and slacks require 4 hrs. Now we have our second constraint.

$\displaystyle \boxed{10c+4s \leq 200}$

We might also assume that some of each will be produced, so we can list the following as constraints as well.

$\displaystyle \boxed{c > 0}$ and $\displaystyle \boxed{s > 0}$

The profit function would be $\displaystyle \boxed{P(x, y)=50c + 40s}$