The cost of producing goods is partly constant and partly varies as the number of goods produced.If 100 and 50 goods cost 65.00 and 285.00 respectively,find the cost of 200 goods
To find the cost of 200 goods, we need to determine the fixed cost and the variable cost per unit.
Let's denote the fixed cost as "FC" and the variable cost per unit as "VC".
From the given information, we know that 100 goods cost $65.00 and 50 goods cost $285.00.
Using this information, we can create two equations:
1. FC + (VC * 100) = $65.00
2. FC + (VC * 50) = $285.00
We can solve this system of equations:
First, subtract equation 2 from equation 1 to eliminate the FC term:
(FC + (VC * 100)) - (FC + (VC * 50)) = $65 - $285
(VC * 100) - (VC * 50) = -$220
VC * 50 = -$220
Next, divide both sides of the equation by 50 to solve for VC:
VC = (-$220) / 50
VC = -$4.40 (cost per unit)
Now, substitute this value of VC into either of the original equations to solve for FC. We'll use equation 1:
FC + (VC * 100) = $65.00
FC + (-$4.40 * 100) = $65.00
FC - $440 = $65.00
FC = $65.00 + $440
FC = $505.00 (fixed cost)
Now that we have determined FC and VC, we can find the cost of producing 200 goods by substituting these values into the equation:
Cost of 200 goods = FC + (VC * 200)
Cost of 200 goods = $505.00 + (-$4.40 * 200)
Cost of 200 goods = $505.00 - $880.00
Cost of 200 goods = -$375.00
Based on the calculations, the cost of producing 200 goods is -$375.00. However, please note that a negative cost is not possible in this context, so there might be an error or inconsistency in the given data.
To find the cost of 200 goods, we need to determine the constant cost and the variable cost per unit.
Let's denote the constant cost as "C" and the variable cost per unit as "V."
From the given information, we know that the total cost of producing 100 goods is $65.00, and the total cost of producing 50 goods is $285.00.
We can set up two equations based on this information:
Equation 1: C + 100V = 65.00
Equation 2: C + 50V = 285.00
To solve these equations, we can use the method of substitution or elimination.
Let's use substitution to solve the system of equations:
1. Solve Equation 1 for C:
C = 65.00 - 100V
2. Substitute the value of C in Equation 2:
(65.00 - 100V) + 50V = 285.00
3. Simplify the equation:
65.00 - 100V + 50V = 285.00
65.00 - 50V = 285.00
4. Move the constant terms to one side:
-50V = 285.00 - 65.00
-50V = 220.00
5. Divide by -50 to solve for V:
V = 220.00 / -50
V = -4.40
Now that we know the variable cost per unit is -4.40, we can substitute this value back into Equation 1 to find the constant cost:
C + 100V = 65.00
C + 100(-4.40) = 65.00
C - 440.00 = 65.00
C = 65.00 + 440.00
C = 505.00
Therefore, the constant cost (C) is $505.00 and the variable cost per unit (V) is -4.40.
To find the cost of 200 goods, we can use the equation:
Total Cost = Constant Cost + (Variable Cost per Unit * Number of Goods)
Total Cost = 505.00 + (-4.40 * 200)
Total Cost = 505.00 - 880.00
Total Cost = -375.00
The cost of producing 200 goods is -$375.00. Please note that a negative value indicates a loss.
cost 65.00 and 285.00 EACH or what ???? I think you have a typo because I would expect the total cost to go down as the number goes up but anyway
c = n * k + b
65 = 100 k + b
285 = 50 k + b
------------------------- subtract
- 220 = 50 k
k = -44
then
65 = -4400 + b
b = 4465
so
c = -44 n + 4465
if n = 200
c = -8800 + 4465