3.5: Chapter 3 Review

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PROBLEM SET: CHAPTER 3 REVIEW

Linear Applications (3.1)

The variable cost to manufacture an item is $30 per item; the fixed costs are $2750. Find the cost function.
The variable cost to manufacture an item is $10 per item, and it costs $2,500 to produce 100 items. Write the cost function, and use this function to estimate the cost of manufacturing 300 items.
In 1990, the average house in Emerald City cost $280,000 and in 2007 the same house cost $365,000. Assuming a linear relationship, write an equation that will give the price of the house in any year, and use this equation to predict the price of a similar house in the year 2020.
A supply curve for a product is the number of items of the product that can be made available at different prices. A doll manufacturer can supply 2000 dolls if the dolls are sold for $30 each, but he can supply only 400 dolls if the dolls are sold for $10 each. If x represents the price of dolls and y the number of items, write an equation for the supply curve.

Fitting Linear Models to Data (3.2)

A random sample of 8 statistics students produced the following data, where $x$ is the Unit 1 Exam score out of 80, and $y$ is the Final Exam score out of 200. A random student earned a 58 on the Unit 1 Exam. If that student follows the class trend, what would you expect this student to earn on the final exam

Table showing the scores on the Final Exam based on scores from the Unit 1 Exam.
$x$ (Unit 1 Exam score)	$y$ (Final Exam score)
65	151
67	133
71	185
75	198
67	153
70	163
71	159
69	159

SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table show different depths with the maximum dive times in minutes. Find the linear regression line and predict the maximum dive time for 110 feet.

$X$ (depth in feet)	$Y$ (maximum dive time)
50	80
60	55
70	45
80	35
90	25
100	22

Maximizing and Minimizing with Linear Programming (3.3 & 3.4)

Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?
A company manufactures two types of cell phones, a Basic model and a Pro model. The Basic model generates a profit of $100 per phone and the Pro model has a profit of $150 per phone. On the assembly line the Basic phone requires 7 hours, while the Pro model takes 11 hours. The Basic phone requires one hour and the Pro phone needs 3 hours for finishing, which includes loading software. Both phones require one hour for testing. On a particular production run the company has available 1,540 work hours on the assembly line, 360 work hours for finishing, and 200 work hours in the testing department. How many cell phones of each type should be produced to maximize profit, and what is that maximum profit?
Jessica needs at least 60 units of vitamin A, 40 units of vitamin B, and 140 units of vitamin C each week. She can choose between Costless brand or Savemore brand tablets. A Costless tablet costs 5 cents and contains 3 units of vitamin A, 1 unit of vitamin B, and 2 units of vitamin C. A Savemore tablet costs 7 cents and contains 1 unit of A, 1 of B, and 5 of C. How many tablets of each kind should she buy to minimize cost, and what is the minimum cost?
A company produces three types of shoes, formal, casual, and athletic, at its two factories, Factory I and Factory II. The company must produce at least 6000 pairs of formal shoes, 8000 pairs of casual shoes, and 9000 pairs of athletic shoes. Daily production of each factory for each type of shoe is given below. Operating Factory I costs $1500 per day and it costs $2000 per day to operate Factory II. How many days should each factory operate to complete the order at a minimum cost, and what is the minimum cost?

	Factory I	Factory II
Formal	100	100
Casual	100	200
Athletic	300	100

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