Question

3. The cost of mass production of cars is partly constant and partly varies as the number of cars produced. The total cost of making 400 cars is sh 3,740,000 and that of making 1000 cars is sh 7,100,000. Find the cost of making 2500cars.

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Answer 1

Explanation:

since the process is defined by a constant term plus a variants term, the equation looks like

costs(c) = k + a×c

3,740,000 = k + 400a

7,000,000 = k + 1000a

let's simply subtract the guys from the second equation

7,000,000 = k + 1000a

- 3,740,000 = -k - 400a

------------------------------------

3,260,000 = 0 + 600a

600a = 3,260,000

a = 5,433.333333... 5,433 1/3

3,740,000 = k + 400×5,433.333333...

k = 3740000 - (400×5,433.333333...) =

= 1,566,666.66666...

so, the function is

costs(c) = 1,566,666.66666... + 5,433.333333... × c

therefore,

costs(2500) =

= 1,566,666.66666... + 5,433.333333... × 2500 =

= sh 15,150,000