Chapter Nineteen Linear Programming

Material $1$ costs $$5$ a pound, material $2$ costs $$4$ a pound, and labor costs $$10$ an hour. Product

A sells for $$80$ a unit, product B sells for $$90$ a unit, and product C sells for $$70$ a unit. Available

resources each day are $200$ pounds of material $1$;$300$ pounds of material $2$ ; and $150$ hours of labor.

The manager must satisfy certain output requirements: The output of product A should not be

more than one$-$third of the total number of units produced; the ratio of units of product $A$ to units

of product B should be $3$ to $2$ ; and there is a standing order for $5$ units of product A each day. For$-$

mulate a linear programming model for this problem, and then solve.