^[8] Deluxe Tire Company finds that to produce each additional tire it costs $21.50. The fixed costs of the plant operation amount to $126,000 per month. The tires are sold for $58 each.

1. Find the revenue and cost functions for the operation.
2. How many tires must be produced and sold in order for Deluxe to break even in a month?
3. How many tires must be produced and sold in order for Deluxe to earn a profit of $40,000 in a month?

 

^[9] A company can rent a car using either of two methods of payment. Method A requires $20 per day and $0.20 per kilometer. Method B requires $35 per day and $0.12 per kilometer.

1. Which method is cheaper for 300 kilometres of use in one day?
2. At what level of use per day are the costing methods equally expensive?
3. A competitor to the company charged $37 for a day’s use during which 80 km were driven, and $43 for a day during which 120 km were driven. Assume the cost function to be linear and find the cost, C, as a function of distance traveled, x.

^[10] Solve the following system of equations for x and y:

y = 2.0 +5.2x

y = 3.0 – 2.0x

 

^[11] Solve the following system of equations for x and y:

y – 4x = 6

2x + 3y = 4

 

^[12] A publishing company finds that, when it prices its computer books at $20 per book, it can sell 7,000 books per month. When it prices them at $25 per book, it can sell 5,500 books per month. The company assumes the relationship is linear.

1. Find the equation which gives the number of books that can be sold per month in terms of the price.
2. How many books should it be able to sell at $22?

 

^[13] FG Company produces housings for a major electrical manufacturer. In a four-week period, during which it produced 2,550 housings, its total costs were $120,000, and in a four-week period, during which it produced 1,750 housings, its total costs were $98,000.

Assume that the costs are linear functions of the number of housings produced each four-week period.

1. Find the equation relating total costs to the number of housings produced in a four-week period.
2. According to your equation in (1), what are the following?
   1. the fixed costs per four-week period
   2. the variable cost per housing
3. If the housings are sold for $55 each, how many must be produced and sold each four-week period in order to break even?
4. Graph your results for costs and revenues. Identify all major areas on the graph.

 

^[14] A furniture company finds that to make a run of 6,200 cabinets costs $205,000 and run of 8,300 costs $267,000.  Assume the relationship between cost and number of cabinets produced is linear.

1. Find the equation which gives cost as a function of number of cabinets produced.
2. If cabinets are sold for $38 each, what is the minimum number of cabinets in a run such that the sales revenue would pay for the cost of the run?

 

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