# Math Help - Linear Programming: Graphical Methods for Minimization Problems and Special Situation

1. ## Linear Programming: Graphical Methods for Minimization Problems and Special Situation

I'm completely lost on this question
1. The Charm City Clothiers Inc. makes coats and slacks. The two resources required are wool cloth and labor. The company has 200 square yards of wool and 300 hours of labor available. Each coat requires 5 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 6 square yards of wool and 4 hours of labor. The profit for a coat is $25, and the profit for a pair of slacks is$15. The company wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

a.Formulate a linear programming model for this problem.
b.Solve this model by hand using the corner points graphical method.

2. Originally Posted by miss holly j
I'm completely lost on this question
1. The Charm City Clothiers Inc. makes coats and slacks. The two resources required are wool cloth and labor. The company has 200 square yards of wool and 300 hours of labor available. Each coat requires 5 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 6 square yards of wool and 4 hours of labor. The profit for a coat is $25, and the profit for a pair of slacks is$15. The company wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

a.Formulate a linear programming model for this problem.
b.Solve this model by hand using the corner points graphical method.
Let x = # slacks made
Let y = # coats made

Total wool cannot exceed 200 sq. yds, so

$5y+6x\leq200$

Total labor cannot exceed 300 hrs, so

$10y+4x\leq300$

Since you cannot make a negative number of slacks and coats,

$y \geq 0 \ \ and \ \ x \geq 0$

Graph each inequality and find the feasible region. Locate the vertices of the feasible region by finding the intersection of the respective linear equations that bound it. Use the profit function P to determine the profit at each vertex. When P is maximized, you have found your optimum production run.

$P=25y+15x$

This would be a whole lot easier if you could use a graphing calculator. Can you?