Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 2 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. 1,000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 200 grates per day. How many grates of each model should the division produce daily to maximize Kane's profits?
Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution. Identify the binding and nonbinding constraints.

A) Produce 100 grates of model A, 100 grates of model B; maximum profit of $504; Range: ; Constraints 2 and 3 are binding; constraint 1 is not.
B) Produce 200 grates of model A, 100 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not.
C) Produce 100 grates of model A, 200 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not.

Question

Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 2 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. 1,000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 200 grates per day. How many grates of each model should the division produce daily to maximize Kane's profits? ​
Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution. Identify the binding and nonbinding constraints.
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A) Produce 100 grates of model A, 100 grates of model B; maximum profit of $504; Range: ; Constraints 2 and 3 are binding; constraint 1 is not. ​ 
B) Produce 200 grates of model A, 100 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not. ​ 
C) Produce 100 grates of model A, 200 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not. ​

Quizplus · Accepted Answer

The Answer of Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 2 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. 1,000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 200 grates per day. How many grates of each model should the division produce daily to maximize Kane's profits? ​
Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution. Identify the binding and nonbinding constraints.
​
A) Produce 100 grates of model A, 100 grates of model B; maximum profit of $504; Range: ; Constraints 2 and 3 are binding; constraint 1 is not. ​ 
B) Produce 200 grates of model A, 100 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not. ​ 
C) Produce 100 grates of model A, 200 grates of model B; maximum profit of $500; Range: ; Constraints 1 and 2 are binding; constraint 3 is not. ​

Kane Manufacturing Has a Division That Produces Two Models of Fireplace