## Mathematical Applications Study Set 1

Statistics

## Quiz 5 :

Inequalities and Linear Programming

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Q11 Q11 Q11

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 4 hours to assemble and 0.5 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 22 per day, and the maximum number of painting hours available is 8 per day. Let x represent the number of deluxe models and y represent the number of economy models. Write the system of inequalities that describes the constraints on the number of each type of wood chipper produced.

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Q12 Q12 Q12

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1 hour to paint, and the economy model requires 2 hours to assemble and 1.5 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 15 per day. Let x represent the number of deluxe models and y represent the number of economy models. Graph the solution of the system of inequalities and find the corners of the solution region.

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Q13 Q13 Q13

An experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments, environment I and environment II. The maximum amount of time available in environment I is 200 minutes, and the maximum amount of time available in environment II is 100 minutes. The white mice must spend 16 minutes in environment I and 20 minutes in environment II, and the rabbits must spend 15 minutes in environment I and 50 minutes in environment II. Write a system of inequalities that describes the constraints on the number of each type of animal used in the experiment. Let x denote the number of white mice and y denote the number of rabbits.

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Q14 Q14 Q14

Suppose that an experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments, environment I and environment II. The maximum amount of time available in environment I is 300 minutes, and the maximum amount of time available in environment II is 400 minutes. The white mice must spend 20 minutes in environment I and 35 minutes in environment II, and the rabbits must spend 45 minutes in environment I and 50 minutes in environment II. Let x represent number of white mice and y represent number of rabbits. Determine the system of inequalities that describes the constraints on the number of each type of animal used in the experiment. Then graph the solution of the system of inequalities.

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Q15 Q15 Q15

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 7 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. Let x represent the number of cord type models and y represent the number of cordless models. Write the inequalities that describe the constraints on the number of each type of hedge trimmer produced.

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Q16 Q16 Q16

A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 6 hours to make, and the cordless model requires 1.5 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. Let x represent the number of cord type models and y represent the number of cordless models. Graph the solution of the system of inequalities.

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Q17 Q17 Q17

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 40 million women and at least 24 million men who are prospective customers. Let x represent the number of minutes of business/investment program commercials and y represent the number of minutes of sporting events commercials. Write the inequalities that describe the constraints on the number of each type of 1-minute spots needed to reach these target groups.

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Q18 Q18 Q18

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 32 million women and at least 20 million men who are prospective customers. Let x represent the number of minutes of business/investment program commercials and y represent the number of minutes of sporting events commercials. Graph the region determined by the constraint inequalities.

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Multiple Choice

Q19 Q19 Q19

The Video Star Company makes two different models of DVD players, which are assembled on two different assembly lines. Line 1 can assemble 32 units of the Star model and 44 units of the Prostar model per hour, and Line 2 can assemble 150 units of the Star model and 40 units of the Prostar model per hour. The company needs to produce at least 260 units of the Star model and 225 units of the Prostar model to fill an order. Let x represent the number of assembly hours for Line 1 and y represent the number of assembly hours for Line 2. Write the inequalities that describe the production constraints on the number of each type of DVD player needed to fill the order.

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Q20 Q20 Q20

The Video Star Company makes two different models of DVD players, which are assembled on two different assembly lines. Line 1 can assemble 30 units of the Star model and 42 units of the Prostar model per hour, and Line 2 can assemble 150 units of the Star model and 40 units of the Prostar model per hour. The company needs to produce at least 250 units of the Star model and 210 units of the Prostar model to fill an order. Let x represent the number of assembly hours for Line 1 and y represent the number of assembly hours for Line 2. Graph the region determined by the constraint inequalities.

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