In planning a new item, a manufactuer assumes that the number of items produced x and the cost of dollars C of producing these items are related by a linear equation, Projections are that 100 items will cost $22,000 to produce. Find the eqaution that relates C and x

This is simple algebra. C100</>=22000=100x

Sorry about trying to getting fancy with fonts. C(output=100) = 22000 = 100x. C(unit=1) per x = (22000/100) = 220

To find the equation that relates C (the cost of producing x items) and x (the number of items produced), we need to use the given information.

The equation relates the cost (C) to the number of items produced (x). We are given that when 100 items are produced, the cost is $22,000.

We can set up the equation as follows:

C = mx + b

Where C is the cost, x is the number of items produced, m is the slope of the line, and b is the y-intercept.

We can substitute the values we know: C = 22000, x = 100.

22000 = 100m + b

To solve for m and b, we need another data point or the value of either m or b.

If we assume the relationship between C and x is linear with a constant slope, we can use the given information to find the slope.

Slope (m) = change in y / change in x = (C2 - C1) / (x2 - x1)

Let's use the given information to find the slope:

C1 = 22000 (when x = 100)
C2 = ?
x1 = 100
x2 = ?

We need another data point to find C2 and x2. Once we have the second data point, we can find the slope.

Let's assume that we have another data point where 200 items are produced, and the cost is $40,000.

C1 = 22000
C2 = 40000
x1 = 100
x2 = 200

Slope (m) = (C2 - C1) / (x2 - x1)
= (40000 - 22000) / (200 - 100)
= 18000 / 100
= 180

Now that we have the slope, we can substitute it back into the equation:

C = mx + b
22000 = 100 * 180 + b
22000 = 18000 + b

To solve for b, we subtract 18000 from both sides:

22000 - 18000 = b
4000 = b

Now we know the value of b, so we can write the equation that relates C and x:

C = 180x + 4000

Therefore, the equation that relates C (the cost of producing x items) and x (the number of items produced) is C = 180x + 4000.