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The Northfork Feed Company makes a feed mix from four ingredients (x1 = pounds of oats, x2 = pounds of corns, x3 = pounds of soybeans, and x4 = pounds of vitamin supplement). The company has 400 pounds of oats, 500 pounds of corn, 300 pounds of soybeans, and 200 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: Constraint 1: At least 20% of the mix must be oats. Constraint 2: At most 30% of the mix must be corns. Constraint 3: The ratio of soybeans to vitamin supplements cannot exceed 3 to 1. Constraint 4: The amount of corns cannot exceed the amount of vitamin supplements. Constraint 5: The mix must be at least 600 pounds. A pound of oats costs $0.40; a pound of corn, $1.50; a pound of soybeans, $0.50; and a pound of vitamin supplement, $3.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.

The Northfork Feed Company makes a feed mix from four ingredients (x1 = pounds of oats, x2 = pounds of corns, x3 = pounds of soybeans, and x4 = pounds of vitamin supplement). The company has 400 pounds of oats, 500 pounds of corn, 300 pounds of soybeans, and 200 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: Constraint 1: At least 20% of the mix must be oats. Constraint 2: At most 30% of the mix must be corns. Constraint 3: The ratio of soybeans to vitamin supplements cannot exceed 3 to 1. Constraint 4: The amount of corns cannot exceed the amount of vitamin supplements. Constraint 5: The mix must be at least 600 pounds. A pound of oats costs $0.40; a pound of corn, $1.50; a pound of soybeans, $0.50; and a pound of vitamin supplement, $3.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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Express constraint 3 to mathematical statement. 

The Northfork Feed Company makes a feed mix from four ingredients (x1 = pounds of oats, x2 = pounds of corns, x3 = pounds of soybeans, and x4 = pounds of vitamin supplement). The company has 400 pounds of oats, 500 pounds of corn, 300 pounds of soybeans, and 200 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: Constraint 1: At least 20% of the mix must be oats. Constraint 2: At most 30% of the mix must be corns. Constraint 3: The ratio of soybeans to vitamin supplements cannot exceed 3 to 1. Constraint 4: The amount of corns cannot exceed the amount of vitamin supplements. Constraint 5: The mix must be at least 600 pounds. A pound of oats costs $0.40; a pound of corn, $1.50; a pound of soybeans, $0.50; and a pound of vitamin supplement, $3.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.
Transcribed Image Text:The Northfork Feed Company makes a feed mix from four ingredients (x1 = pounds of oats, x2 = pounds of corns, x3 = pounds of soybeans, and x4 = pounds of vitamin supplement). The company has 400 pounds of oats, 500 pounds of corn, 300 pounds of soybeans, and 200 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: Constraint 1: At least 20% of the mix must be oats. Constraint 2: At most 30% of the mix must be corns. Constraint 3: The ratio of soybeans to vitamin supplements cannot exceed 3 to 1. Constraint 4: The amount of corns cannot exceed the amount of vitamin supplements. Constraint 5: The mix must be at least 600 pounds. A pound of oats costs $0.40; a pound of corn, $1.50; a pound of soybeans, $0.50; and a pound of vitamin supplement, $3.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.
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