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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 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 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 = $ 10 X at (x, y) = 20 3 0,5 (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? 20 The optimal profit is P = $10 x at (x, y) = (0, * ). 3

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 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 = $ 10 X at (x, y) = 20 3 0,5 (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? 20 The optimal profit is P = $10 x at (x, y) = (0, * ). 3

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.2: Systems Of Linear Equations: Three Variables
Problem 61SE: Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one...
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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 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 = $ 10 X at (x, y) = (0, 20 3 (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? 20 The optimal profit is P = $ 10 × at (x, y) = (0, * ). 3
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 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 = $ 10 X at (x, y) = (0, 20 3 (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? 20 The optimal profit is P = $ 10 × at (x, y) = (0, * ). 3
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