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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 Ib 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 Ib 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 $1.50/grate, what will be the optimal profit? The optimal profit is P = $ 420 at (x, y) = 120,160 (b) If the contribution to the profit of a model A grate is changed to $3.00/grate, what will be the optimal profit? The optimal profit is P = $ 600 V at (x, y) = 200,0

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 Ib 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 Ib 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 $1.50/grate, what will be the optimal profit? The optimal profit is P = $ 420 at (x, y) = 120,160 (b) If the contribution to the profit of a model A grate is changed to $3.00/grate, what will be the optimal profit? The optimal profit is P = $ 600 V at (x, y) = 200,0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 Ib of cast iron and 6 min of labor. To produce each model B grate requires 4 Ib of cast iron and 3 min labor. The profit for each model A grate is $2, and the profit for each model B grate is $1.50. 1000 Ib 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 $1.50/grate, what will be the optimal profit? The optimal profit is P = $ 420 at (x, y) = 120,160 (b) If the contribution to the profit of a model A grate is changed to $3.00/grate, what will be the optimal profit? The optimal profit is P = $ 600 at (x, y) = 200,0
Transcribed Image Text: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 Ib of cast iron and 6 min of labor. To produce each model B grate requires 4 Ib of cast iron and 3 min labor. The profit for each model A grate is $2, and the profit for each model B grate is $1.50. 1000 Ib 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 $1.50/grate, what will be the optimal profit? The optimal profit is P = $ 420 at (x, y) = 120,160 (b) If the contribution to the profit of a model A grate is changed to $3.00/grate, what will be the optimal profit? The optimal profit is P = $ 600 at (x, y) = 200,0
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