1. It is known that the cost function of a company is a linear function. Further

Question

1. It is known that the cost function of a company is a linear function. Further the fixed cost of the company is $20,000 and the total cost of producing 10 items is $25,000. Find the cost function of the company.

2. A cable TV company charges $23 for the basic service plus $6 for each movie channel. Let C(x) be the total cost in dollars of subscribing to cable TV, using x movie channels. Find the linear cost function.

3. A cab company charges a base rate of $2.00 plus 20 cents per minute. Let C(x) be the cost in dollars of using the cab for x minutes. Find the linear cost function.

4. A new car was purchased for $14,500, and 3 years later it was worth $9100. Assume that the depreciation in value is given by a linear equation. Find the equation, if y is the value of the car after x years.

5. Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $50,000 in 2008 and $80,000 in 2013. Let x = 0 represent the year 2008. Find the equation giving yearly sales S(x).

Explanation / Answer

1) cost function: cost = 20000 + (x/10) * 25000 where x is number of items produced

2) C(x) = 6*x + 23

3) C(x) = 20*x +200

4) let y = ax+b

so b = 14500 since y = b when x =0

and 9100 = 3a + 14500 so we get a = -1800

so it is: y= -1800x + 14500

5) y = ax+b be the sales equation

when x =0, y=b = 50k

when x=5, 80k = 5a + 50k so a = 6k

S(x) = 6000x + 50000

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