Help I can go this far and then lost.
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 items will cost $10,000to produce and the 300 items will cost $22,000 to produce. Find the equation that relates C and x
Cost = K1 * n + K2
n= 100
n = 300
from here I'm lost
Well, you know the cost for each of those n.
10000=k1*100 + k2
22000=k1(300)+k2
solve for the constants.
To find the equation that relates the cost (C) and the number of items produced (x), you can use the given information to solve for the constants K1 and K2 in the equation Cost = K1 * x + K2.
Given that 100 items will cost $10,000 to produce, you can substitute this information into the equation:
10,000 = K1 * 100 + K2
Similarly, 300 items will cost $22,000 to produce, so you can substitute this information into the equation as well:
22,000 = K1 * 300 + K2
Now, you have two equations with two unknowns (K1 and K2). To find the values of K1 and K2, you can solve these equations simultaneously.
One approach is to use the method of substitution. Solve one equation for one of the variables and substitute it into the other equation. Then solve for the remaining variable.
Let's solve the first equation for K2:
10,000 = K1 * 100 + K2
Rearranging the equation, we get:
K2 = 10,000 - K1 * 100
Now substitute this expression for K2 into the second equation:
22,000 = K1 * 300 + (10,000 - K1 * 100)
Now, simplify the equation:
22,000 = K1 * 300 + 10,000 - K1 * 100
Combining like terms, we have:
22,000 = 200K1 + 10,000
Simplify further:
12,000 = 200K1
Now solve for K1:
K1 = 12,000 / 200
K1 = 60
Substitute this value of K1 back into either of the original equations to find K2:
10,000 = 60 * 100 + K2
Simplifying:
10,000 = 6,000 + K2
K2 = 10,000 - 6,000
K2 = 4,000
So the equation that relates the cost (C) and the number of items produced (x) is:
Cost = 60x + 4,000