Question
In: Math
Kane Manufacturing has a division that produces two models of fireplace grates, x units of model...
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 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 $2.00, and the profit for each model B grate is $3.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had 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?
Solutions
Expert Solution
Given, Kane Manufacturing produces two models of fireplace grates, x units of model A and y units of model B.
By the given conditions, the problem becomes,
Maximize z = 2x+3y (total cost)
subject to 3x+4y 
1000
6x+3y 1200
x+y 
150
x,y 0
Kane should produce 0 units of model A and 250 units of model B to maximize profit.
milcah answered 1 year agoRelated Solutions
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