Planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C.

Question

Planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates to C and x?

Answer 1

Linear equations are of the form A = Bx + C

In this case, Total Cost = Price ea. x Nunber of items + Konstant .. (I'm using K for the coinstant to avoid confusion with C for Total Cost)

So we have :-
10,000 = 100 * Price ea. + Konstant
22,000 = 300 * Price ea. + Konstant

2 equations suffice to discover 2 unknowns (Price each & Konstant) so from here it's easy ..

Solving for Price each ...

10000 = 100p + K, K= 10000 - 100p
22000 = 300p + K, K= 22000 - 300p

So 10000 - 100p = 22000 - 300p
300p - 100p = 22000 - 10000
200p = 12000
p = 12000/200, p = 60

Back substituting in K = 10000 - 100p we have
K = 10000 - 100 x 60, K = 1000 - 6000, K = 4000

We thus have .. Total Cost (C) = 60x + 4000
(where x = number of units).

OK ?