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Econ 407: Warming up: 2

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1. A hot-dog stand starts with 200 hotdogs and is sold out after 5 hours. If the relationship between hot-dogs sold and an hour is linear equation, figure out the relationship between the two variables. After how many hours there will be 40 hot-dogs left?

2. A woman buys a car for $3800, and after 2 years it is worth $3000. Find the relationship between the year and the value of the car if it is represented by a linear equation. How much will the car be worth 7 years after the day of purchase?

3. Maple Inc. stock went on sale at $3.20 per share, and after 3 months the price was $3.75. Find the relationship between the month and the stock price if it is represented by a linear equation. How much will this stock be worth in 1 year?

4. Let R(x) and C(x) denote the revenue and cost functions for a company as discussed in Application 3. From the following problems, find the number of items the company must sell before it begins to show a profit.

a. C(x) = x/3 + 6,

R(x)=x

b. C(x)= x+3,

R(x)=3x


c. C(x)= 2x/5 + 4,

R(x)= 2x-2


d. C(x) = x/2 + 7,

R(x) = 3x - 6

For each of the above cases, graph the profit function.