Calculate fixed cost and variable cost per unit by using least square method. X = 150,000 Y = Rs. 2,500,000 XY = Rs. 85,000,000 X^2 = 5,500,000 N = 5

To calculate the fixed cost (FC) and variable cost per unit (V) using the least squares method, we use the following formulas:

$$Y=a+bX$$ where:

• $Y$ = Total Cost
• $X$ = Number of units
• $a$ = Fixed Cost (FC)
• $b$ = Variable Cost per unit (V)

The normal equations for least squares are:

$$b=\frac{N\Sigma XY-\Sigma X\Sigma Y}{N\Sigma X^2-(\Sigma X{)}^2}$$

$$a=\frac{\Sigma Y-b\Sigma X}{N}$$

Step 1: Calculate $b$ (Variable Cost per unit)

$$b=\frac{(5\times 85,000,000)-(150,000\times 2,500,000)}{(5\times 5,500,000)-(150,000{)}^2}$$

$$b=\frac{425,000,000-375,000,000}{27,500,000-22,500,000}$$

$$b=\frac{50,000,000}{5,000,000}=10$$

Step 2: Calculate $a$ (Fixed Cost)

$$a=\frac{2,500,000-(10\times 150,000)}{5}$$

$$a=\frac{2,500,000-1,500,000}{5}=\frac{1,000,000}{5}=200,000$$

Final Answer:

• Fixed Cost (FC) = Rs. 200,000
• Variable Cost per unit (V) = Rs. 10