^[15] For a certain good there is a demand for 8,000 units when the price is $8/unit and a demand for 6,200 when the price is $12/unit. Assuming demand, d, is a linear function of price, p, find the slope of the line and the equation.

 

^[16] HJ Outdoor Company found that it cost $6,100 to make a run of 105 jackets, and $7,900 to make a run of 150 jackets. Assume the cost is a linear function of the number of jackets made.

1. Find the cost as a function of the number of jackets made in a run, and graph it from 80 to 200 jackets.
2. Estimate the cost of a run of 180 jackets.
3. If HJ sells the jackets for $55 each, how many must be in a run in order to barely recover the cost of making the jackets?

^[17] Find the equation of the line:

1. with slope 3 that contains the point (4, 1).
2. with slope -5 that contains the point (-2, 3).
3. containing the points (2, 3) and (-6, 1).
4. containing the points (12, 16) and (1, 5).
5. containing the points (-4, 5) and (-2, -3).
6. that contains the point (-4, 2) and falls 2 units in y for every one unit increase in x.

 

^[18] You use your calling card to make a telephone call to your friend who lives in Oyster River. You receive your monthly telephone bill and two of the items are as follows:

1. Define the two variables and create an equation to calculate the total cost of a call.
2. How much would a 60-minute call cost?

 

^[19] You have been asked to predict the cost of flying a Dash 7 aircraft from Vancouver to Seattle. You are provided with the following information:

 

1. Define the two variables and create an equation to calculate the total cost of a flight.
2. How much would it cost to fly the plane empty (with no passengers)?
3. Interpret the y intercept using the words of the problem.
4. How much extra does it cost to have one more passenger?
5. Interpret the slope using the words of the problem.
6. How much would it cost to fly 14 passengers?

 

^[20] B. Furniture Co. believes that the cost to produce its chairs is a linear function (straight line relationship) of the number of chairs to be produced in a run. It finds that to produce a run of 130 chairs requires $8,200, and that a run of 250 chairs requires $13,000.

1. Find the equation giving cost, C, based on the number of chairs produced, x, in a run.
2. What is the cost if no chairs are produced?
3. Interpret the y intercept using the words of the problem.
4. What is the extra cost to make one more chair?
5. Interpret the slope using the words of the problem.
6. How much would it cost to produce 400 chairs?
7. How many chairs can be expected to be produced with a run that is assigned $8,600?

 

^[21] Mr. Smith wants to rent a truck for one day to make a number of deliveries. He can rent the type of truck he needs from either of two companies. Company A charges $100 plus $0.40 per kilometre. Company B charges $40 plus $0.80 per kilometre.

1. Write equations for the cost, C, of each truck in terms of x, the number of kilometres traveled.
2. Suppose you rent a truck from Company A,
   1. How much would it cost to rent the truck but not actually drive it (0 km)?
   2. How much would it cost to drive 300 kilometres?
3. Suppose you rent a truck from Company B,
   1. How much would it cost to rent the truck but not actually drive it (0 km)?
   2. How much would it cost to drive 300 kilometres?
4. Graph the equations on the same axes and show on the graph where each company’s deal is best. Graph from 0 to 300 km. Use a large scale, graph paper and straight edge, and apply proper conventions.
5. Using your graph, determine the point where the costs are equal. Mark the point on the graph you made in (4).

 

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