In 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 itmes will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
10000=K + m 100
22000=K+ m 300
solve for K and M. I would start by subtracting the first equation from the second solving for m.
10000=K + m 100
22000=K+ m 300
solve for K and M. I would start by subtracting the first equation from the second solving for m.
To find the equation that relates the cost C and the number of items produced x, we need to solve the system of equations:
10000 = K + m * 100 -- Equation 1
22000 = K + m * 300 -- Equation 2
To isolate m, we subtract Equation 1 from Equation 2:
22000 - 10000 = K + m * 300 - (K + m * 100)
12000 = m * 300 - m * 100
12000 = 200m
Solving for m:
m = 12000 / 200
m = 60
Now that we have the value of m, we can substitute it back into either equation to find the value of K. Let's use Equation 1:
10000 = K + 60 * 100
10000 = K + 6000
Subtracting 6000 from both sides:
K = 10000 - 6000
K = 4000
Therefore, the equation that relates the cost C and the number of items produced x is:
C = 4000 + 60x