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, and the profit for each model B grate is $1.50. 1000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model B grates, management has decided to limit the production of model B grates to no more than 200 grates per day. (a) If the contribution to the profit of a model A grate is changed to $1.25/grate, what will be the optimal profit? The optimal profit is P = $ at (x, y) = . (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? The optimal profit is P = $ at (x, y) =
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, and the profit for each model B grate is $1.50. 1000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model B grates, management has decided to limit the production of model B grates to no more than 200 grates per day.
(b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit?
As per the question we are given a model of the Manufacturing is a company with a division that produces two models of fireplace grates - Model A and Model B. There are constraints on the amount of cast iron and labor available for production each day, as well as a production limit on Model B grates. The profit for each Model A grate is $2 and the profit for each Model B grate is 1.5.
Now we have to construct the linear optimization problem and find the optimal solution in case of :
(a) the contribution to the profit of a Model A grate is changed to $1.25/grate.
(b) the contribution to the profit of a Model A grate is changed to $2.25/grate.
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