A toy company produces 2 models of water guns: spray king and zapper. They are manufactured in batches for easier packaging and sale. Two of the limiting resources are 1200 pounds of special plastic material available a week to make two models, and 40 hours of production time that are available each week.
The spray king model requires 2 pounds of plastic per batch, while zapper needs 1 pound of plastic per batch. Production time in minutes per batch for spray king is 3 minutes. Each batch of zapper requires 4 min of production time.
The profit from each batch of spray king is $8. For zapper, the profit is $5 per batch. The company's objective is maximize weekly profit.
A manufacturing restriction is that the weekly production of spray king cannot exceed the weekly production zapper by more than 450 batches. This is referred to as the "mix" constraint. Also, the total weekly production for the two models combined cannot exceed 800 batches each week. This is referred to as the "total production" constraint.
Use the following variable:
X_{1}= Number of batches of spray king manufactured each week
X_{2}=Number of batches zapper manufactured each week
1. ) determine the Linear Programming model that represents the describes scenario.
2.) To maximize profit, what is the number of batches that should be produced weekly?
3.)Calculate the maximum weekly profit
4.) If the profit per batch of zapper falls to $4, in order to have (i) multiple optimal solutions, and (ii) the profit per batch of zapper be less than that of spray king, the profit per batch of bag of spray king should be
A.) $2.00 B.) $10.00
C.) $8.00 D.) $5.00
5.) What is the binding constraints for the original linear program model?