word problem!!?

Question

In planning for a new item, a manufacturer assumes that the number of an item produced x and the cost in dollars C producing these items are related by a liner equation. projections are that 100 items will cost 10,000 dollars to produce, and 300 items will cost 22,000 to produce.find the equasion that relates C and X.?

Answer 1

Your equation will have the form c=a+bx (because it is assumed linear) C=cost and x=number of items
We know that 10000=a+b(100) and 22000=a+b(300)
From the first equation we find a=10000-100b and replace it in the second equation. 22000=300b+10000-100b so 200b=12000 so b=12000/200=60
To find a we replace in the first equation 10000=a+60(100) so a=4000
Your equation is C=4000+60x

Answer 2

Let C = F + xV, where F is the "fixed cost" (independent of the number of units produced) and V is the "variable cost".

Since C=10,000 when x=100 and C=22,000 when x=300, you have these two equations for the unknowns F and V:

F + 100V = 10000
F + 300V = 22000

Subtract the first equation from the second, and you get 200V=12000, so V=60.

Substitute this value of V into either equation to get F:

F + 100*60=10000, so F=4,000.

Answer 3

You can readily determine the slope of the equation by

(22000 - 10000)/(300 - 100) = 12000/200 = 60

Using either of the known points, you can determine the y-intercept

y = 60X + b
10000 = 60(100) + b
10000 = 6,000 + b
4000 = b

y = 60X + 4000 is the desired equation

See if true for the other known point

22000 = 60(300) + 4000
22000 = 18000 + 4000
22000 = 22000