cKathryn Bollinger, September 5, 2011 1Week-In-Review #1 (1.2 [Review], 1.3, 1.4, 1.5)1. Find the equation of the line that passes throug h the point (−1, 2) and(a) has slope = 5/2.(b) also passes through the point (3, −4).(c) ha s slope = 0.(d) has undefined slope.2. Find the equation of the line which crosses the x-axis at 2 and the y-axis at −3.3. The Acme Widget Co. produces regular and deluxe widgets out of wood. Each regularwidget requires 2 units of wood; each deluxe widget requires 4 units o f wood. There are 600units of wood available for production each week.(a) Assuming that all available units of wood are used up each week, write down a linearequation in general form (Ax + By + C = 0) relating the number of regulars produced(x) a nd the number of deluxes produced (y).(b) Write the equation in slope-intercept form (y = mx + b).(c)(i) If the co. wants to make 10 less regulars, what does that do to the production ofdeluxes?(ii) If the co. wants to make 10 less deluxes, what does that do to the production ofregulars?(iii) In general, how are the production levels of the different widgets related?(d) What are the maximum number of regulars that may be produced? D eluxes? How dothese maximums appear in the graph of the equation?4. A compressor wa s bought for $9,000. According to the depreciation schedule, the valueof the compressor will drop by the same amount every year until 10 years have passed, atwhich po int the compressor has only salvage, or scrap, value. The value of the compressorafter two years is $7,300.(a) Find V (t), the value of the machine after t years. (0 ≤ t ≤ 10)(b) What is the rate of depreciation of the compressor?(c) What is the salvage, or scrap, value of the compressor?(d) Determine the value of the compressor after 15 years.cKathryn Bollinger, September 5, 2011 25. A company making keys has fixed costs of $1 5,000 each month. It costs this company $1to make each key and each key sells for $ 5.(a) Find the linear cost, revenue, and profit functions for this company.(b) How much will the company profit if 2500 keys ar e made and sold?(c) How many keys must be sold in a month in order to have a profit of $10,000?(d) How many keys must be sold in a month in order for this company to make a profitgain?6. A gadget company finds that the daily total cost of producing 200 gadgets is $14,00 0.It a lso finds that if no gadgets are produced, the company still has a daily cost of $ 10,000.Each gadget sells for $26.(a) What is the production cost per gadget?(b) Find the company’s linear cost, revenue, and pro fit f unctions.(c) Find the break-even point for the co. and explain it s meaning.Is this a “true” break-even point?7. A manufacturer of timers, has a monthly fixed cost of $ 48,000 and a pro duction cost of$8 for each timer manufactured.(a) What is the selling price of the timers, if the company has a profit of $112,000 whenselling 5,000 timers?(b) What is the profit function for the company?8. Given x = the number of figurines supplied or demanded per month and p = unit priceof the figurines in dollars and Equation 1 is −5x + 2p = 60 a nd Equation 2 is 3x + 2p = 300,answer the following:(a) Which equation is the demand equation? Why?(b) How many units will consumers demand if the figurines are free?(c) What is the highest price consumers a re willing to pay for the figurines?(d) Suppliers will only provide the figurines if the price is above what value?(e) Find the equilibrium point for the market and write a sentence explaining the meaningand importance of the values of the coordinates of this point, in the context of theproblem.cKathryn Bollinger, September 5, 2011 39. Suppliers will market 500 books when the unit price is $25. Consumers will demand10,000 books if they are free. For each dollar rise in the price of a book, consumers willdemand 200 fewer books, while producers will supply 100 additional books.(a) Find the linear demand and supply equations.(b) What is the equilibrium point for the book market? Explain its meaning.10. On the planet of Mathetopia, city populations and newspaper readership were deter-mined. The f ollowing table gives the population of a city (in millions of people) vs. thenumb er of people who read the newspaper in the city (in hundreds of people):Population0.52 0.78 1.33 1.85 2.46Readers 75 128 135 175 200(a) Determine the equation of the least- squares line for this da t a. Round all coefficients/constantsto four decimal places.(b) Is this a good representation of the data? Why or why not?(c) Interpret the slope of your model.(d) Estimate the number of newspaper readers, to the nearest person, when the city has apopulation of 9 58,000.(e) Determine the population of a city, to the nearest person, if the newspaper readershipis found to be 35,000
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