The problem states:
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 $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and X.
This is what i did:
THe two points relating C and X: (100,10000) and (300,22000)
m= (22000-10000)/(300-100)=
(12000)/(300)=60
Using one of the point values for x and C and m=60 i can then solve for "B"
10000=60(100)+b
b=10000-6000=4000
Equation would be: Cost = 60x+4000
First of all, the slope is 60 but you typed (12000)/(300) and it should be (12000)/(200). The rest is right.
To find the equation that relates the cost C and the number of items produced X, you need to use the two points given: (100, 10000) and (300, 22000).
Step 1: Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
For the two points (100, 10000) and (300, 22000), the calculation is:
m = (22000 - 10000) / (300 - 100)
m = 12000 / 200
m = 60
Step 2: Plug in the slope (m) into the equation: y = mx + b, where b is the y-intercept.
Using one of the points (100, 10000):
10000 = 60(100) + b
10000 = 6000 + b
b = 10000 - 6000
b = 4000
Step 3: Substitute the slope (m) and the y-intercept (b) back into the equation: y = mx + b
Cost = 60x + 4000
So, the equation that relates the cost C and the number of items produced X is Cost = 60x + 4000.