A manager wants to know how many units of each product to produce on a daily basis in order toachieve the highest contribution to profit. Production requirements for the products are shown inthe following table.ProductMaterial 1(pounds)Material 2(pounds)Labor(hours)A 2 3 3.2B 1 5 1.5C 6 — 2.0Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product Asells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Availableresources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not bemore than one-third of the total number of units produced; the ratio of units of product A to units ofproduct B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve
A manager wants to know how many units of each product to produce on a daily basis in order to
achieve the highest contribution to profit. Production requirements for the products are shown in
the following table.
Product
Material 1
(pounds)
Material 2
(pounds)
Labor
(hours)
A 2 3 3.2
B 1 5 1.5
C 6 — 2.0
Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product A
sells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Available
resources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not be
more than one-third of the total number of units produced; the ratio of units of product A to units of
product B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve
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