Kane Manufacturing has a division that produces two models of fireplace 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. 1,000 lb of cast iron and 23 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? The range of values that the coefficient of x can assume without changing the optimal solution is 1.125 ≤ c ≤ 3.

If the contribution to the profit of a model A grate is changed to $2.05/grate, will the original optimal solution still hold? Answer yes or no. __________

What will be the new optimal solution?

Model A: __________

Model B: __________

Please enter your answer as a dollar value to the nearest cent:

maximum profit: $ __________

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 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. 1,000 lb of cast iron and 23 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? The range of values that the coefficient of x can assume without changing the optimal solution is 1.125 ≤ c ≤ 3.
​
If the contribution to the profit of a model A grate is changed to $2.05/grate, will the original optimal solution still hold? Answer yes or no. __________
​
What will be the new optimal solution?
​
Model A: __________
​
Model B: __________
​
Please enter your answer as a dollar value to the nearest cent:
​
maximum profit: $ __________

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 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. 1,000 lb of cast iron and 23 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? The range of values that the coefficient of x can assume without changing the optimal solution is 1.125 ≤ c ≤ 3.
​
If the contribution to the profit of a model A grate is changed to $2.05/grate, will the original optimal solution still hold? Answer yes or no. __________
​
What will be the new optimal solution?
​
Model A: __________
​
Model B: __________
​
Please enter your answer as a dollar value to the nearest cent:
​
maximum profit: $ __________

Kane Manufacturing Has a Division That Produces Two Models of Fireplace