Question

"Let A = the number of model A grates and let B = the number of model B clock grates. In this application, write the constraint for the number of pounds of iron: Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2, and the profit for each model B grate is $1.50. Available for grate production each day are 100 lb of cast iron and 20 hr of labor. 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 profits?"

Answer 1

Answer:

In this problem, if we solve it by linear programming one of the conditions does not satisfy which is - number of B should be produced at least 180 in order to meet backlog. This means for B only we need 180* 4 = 540 lbs of iron where as daily supply is only of 100 lbs.

for this option (3) looks viable i.e. 3A + 4B <= 100