Question

Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast iron and 8 min of labor. To produce each model B grate requires 5 lb of cast iron and 5 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. 1200 lb of cast iron and 1500 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars

Answer 1

Answer:

The company will produce the requested 150 units of A for a gain of 300 dollars

and then use his resourses to produce B yielding a gain of 90 dollars

total of 390 profit

Explanation:

The company will produce at least 150 units of product A therefore:

lbs used: 150 x 3 = 450

minutes of labor used 150 x 8 = 1,200

leaving available:

1,200 - 450 = 750 lbs

1,500 - 1,200 = 300 mins

As time is the most scarce resource we allocate base on thecontribution per minute:

product A $2 of profit for 8 minutes: 0.25 dollars per minute

product B $1.5 of profit for 5 minutes: 0.30 dollars per minute

As product B is more profitable considering labor time we use the entire amount left to produce product B

300 min / 5 minutes = 60 units of b