^[1] Ocean Marina rents moorage space for boats. Its charge for boats between 20 and 40 feet long is $180 plus $12 a foot.

Let  x = boat length in feet C = cost of moorage:

x	20	24	28	32	36	40
C

1. Complete the above table relating length and cost.
2. State the equation describing cost as a function of length.
3. Graph cost as a function of length for 20 to 40 feet.

 

^[2] An agent has available truck shipping capacity for 62.5 tons of materials A and B. Each unit of A weighs 2.4 tons and each unit of B weighs 1.7 tons. Find an equation that relates the amounts of A and B that can be shipped.

 

^[3] A company finds that when the temperature is 12°C it uses 100 litres of heating oil per day. When the temperature is 5°C, it uses 170 litres of heating oil per day.

1. Mark the above data points on a graph (allow for negative temperatures).
2. Find the equation (assumed to be linear) for oil usage in terms of temperature.
3. Find the amount of oil that would be used at -5°C. Check your result on a graph.

 

^[4] A company has a choice between two copiers, A and B. A costs $120 a month plus $0.05 per page; B costs $250 a month plus $0.03 per page.

1. Find the cost equations for each copier.
2. Which copier would be best for 5,000 pages a month? For 10,000 copies?
3. Graph the equations on the same axes and show clearly where each copier is cheapest.
4. Find the volumes at which the costs are equal and mark the point on your graph.

 

^[5] Jones Stereo Company sells stereo sets for $150 each. The parts for each stereo cost $39.50 and the labor costs $53 per set. Fixed costs are $16,000 a month.

1. Find Jones’ cost and revenue functions.
2. How many must Jones produce and sell every month in order to (i) break even? (ii) make a $6,000 profit?

^[6] Find the equations of the following lines.

1. Passing through (3, 10) and (1, 6).
2. With slope 1.5 and passing through (2, 5).
3. Passing through (1, 7) and falling 2 units in for each increase of 1 in x.

 

^[7] Jimms Company believes that the time required to produce its widgets is a linear function of the number of widgets to be produced in a run. It finds that to produce a run of 600 widgets requires 7,050 minutes, and that to produce a run of 350 widgets requires 4,300 minutes.

1. Find the equation giving time required as a function of the number of widgets.
2. How long will it take to produce 500 widgets?
3. How many widgets can one expect to produce with a run that is assigned 81 hours?

 

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