Chapter 3.CRE, Problem 17CRE

PRODUCTION SCHEDULING Kane Manufacturing has a division that produces two models of grates, model 
 $A$ and model 
 $B$. To produce each model 
 $A$ grates requires 
 $3\text{lb}$ of cast iron and 6 min of labor. To produce each model 
 $B$ grates requires 
 $4\text{lb}$ of cast iron and 3 min of labor. The profit for each model 
 $A$ grates is 
 $\$2.00$, and the profit for each model 
 $B$ grates is 
 $\$1.50$. Available for grate production each day are 
 $1000\text{lb}$ of cast iron and 20 labor – hours. Because of a backlog of orders for model 
 $B$ grates, Kane’s manager has decided to produce at least 180 model 
 $B$ grates per day. How many grates of each model should Kane produce to maximize its profit? What is the maximum profit?