a. Apex Motors manufactures luxury cars and sport-utility vehicles. The most likely customers are high-income men and women, and company managers want to initiate an advertising campaign targeting these groups. They plan to run 1-minute spots on business/investment programs, where they can reach 7 million women and 4 million men from their target groups. They also plan 1-minute spots during sporting events, where they can reach 2 million women and 12 million men from their target groups. Apex feels that the ads must reach at least 37 million women and at least 32 million men who are prospective customers. A) 0.18x + 0.75y ≤ 1020 0.3x ≤ 630 0.2x + 0.2y ≥ 500 x ≥ 0, y ≥ 0 B) 7x+2y ≥ 37 4x + 12y ≥ 32 x ≥ 0, y ≥ 0 C) 0.6x + 0.4y ≤ 3200 0.2x + 0.2y ≥ 1200 0.2y ≤ 1000 x ≥ 0, y ≥ 0 D) 2x + 6y ≤ 600 x + y ≤ 200 x ≥ 0, y ≥ 0 b. A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day. A) 7x+2y ≥ 37 4x + 12y ≥ 32 x ≥ 0, y ≥ 0 B) 0.18x + 0.75y ≤ 1020 0.3x ≤ 630 0.2x + 0.2y ≥ 500 x ≥ 0, y ≥ 0 C) 0.6x + 0.4y ≤ 3200 0.2x + 0.2y ≥ 1200 0.2y ≤ 1000 x ≥ 0, y ≥ 0 D) 2x + 6y ≤ 600 x + y ≤ 200 x ≥ 0, y ≥ 0 c. A sausage company makes two different kinds of hot dogs, regular and all beef. Each type of hot dog uses some ingredients that are always available, but supplies of beef, pork, and spices are limited. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 630 lb of pork, and at least 500 lb of spices. A) 2x + 6y ≤ 600 x + y ≤ 200 x ≥ 0, y ≥ 0 B) 0.6x + 0.4y ≤ 3200 0.2x + 0.2y ≥ 1200 0.2y ≤ 1000 x ≥ 0, y ≥ 0 C) 7x+2y ≥ 37 4x + 12y ≥ 32 x ≥ 0, y ≥ 0 D) 0.18x + 0.75y ≤ 1020 0.3x ≤ 630 0.2x + 0.2y ≥ 500 x ≥ 0, y ≥ 0 d. A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched syrup. Suppliers can deliver at most 3200 lb of wheat, at most 1000 lb of sugar, and at least 1200 lb of the vitamin-enriched syrup. A) 7x+2y ≥ 37 4x + 12y ≥ 32 x ≥ 0, y ≥ 0 B) 0.18x + 0.75y ≤ 1020 0.3x ≤ 630 0.2x + 0.2y ≥ 500 x ≥ 0, y ≥ 0 C) 0.6x + 0.4y ≤ 3200 0.2x + 0.2y ≥ 1200 0.2y ≤ 1000 x ≥ 0, y ≥ 0 D)2x + 6y ≤ 600 x + y ≤ 200 x ≥ 0, y ≥ 0
a. Apex Motors manufactures luxury cars and sport-utility vehicles. The most likely customers are high-income men and women, and company managers want to initiate an advertising campaign targeting these groups. They plan to run 1-minute spots on business/investment programs, where they can reach 7 million women and 4 million men from their target groups. They also plan 1-minute spots during sporting events, where they can reach 2 million women and 12 million men from their target groups. Apex feels that the ads must reach at least 37 million women and at least 32 million men who are prospective customers.
b. A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day.
c. A sausage company makes two different kinds of hot dogs, regular and all beef. Each type of hot dog uses some ingredients that are always available, but supplies of beef, pork, and spices are limited. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 630 lb of pork, and at least 500 lb of spices.
d. A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched syrup. Suppliers can deliver at most 3200 lb of wheat, at most 1000 lb of sugar, and at least 1200 lb of the vitamin-enriched syrup.
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