Calculate the fixed and variable elements of the above mixed factory overhead using: i. The high and low method; ii. The linear regression analysis and determine the line of best fit.

Question

Asked on August 25, 2026Business/Management

This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.

Accepted Answer · 2026-08-25T15:45:58.133Z

Here's how to calculate the fixed and variable elements of the mixed factory overhead using the requested methods. i) The high and low method Step 1: Identify the high and low activity levels and their corresponding overhead costs. From the table: • Highest activity: July, 350 units, Overhead = 140 • Lowest activity: January and October, 150 units, Overhead = 80 Step 2: Calculate the variable cost per unit. The formula for variable cost per unit is: Variable Cost Per Unit = Highest Overhead Cost - Lowest Overhead CostHighest Activity Level - Lowest Activity Level Substitute the values: Variable Cost Per Unit = (140 - 80)/(350 - 150) = (60)/(200) = 0.30 The variable cost per unit is 0.30. Step 3: Calculate the total fixed cost. Total fixed cost can be found by taking the total cost at either the high or low activity level and subtracting the total variable cost at that level. Using the high activity level (July): Total Fixed Cost = Total Overhead at High Activity - (Variable Cost Per Unit × High Activity Level) Total Fixed Cost = 140 - (0.30 × 350) = 140 - 105 = 35 Using the low activity level (January/October): Total Fixed Cost = Total Overhead at Low Activity - (Variable Cost Per Unit × Low Activity Level) Total Fixed Cost = 80 - (0.30 × 150) = 80 - 45 = 35 The fixed cost is 35. ii) The linear regression analysis and determine the line of best fit Step 1: Set up the data for linear regression. We need the sum of x, y, xy, x^2, and the number of observations (n). | Month | Units (x) | Overhead (y) | x^2 | xy | | :-------- | :-------- | :----------- | :------ | :------ | | January | 150 | 80 | 22500 | 12000 | | February | 200 | 100 | 40000 | 20000 | | March | 300 | 135 | 90000 | 40500 | | April | 250 | 125 | 62500 | 31250 | | May | 300 | 130 | 90000 | 39000 | | June | 250 | 120 | 62500 | 30000 | | July | 350 | 140 | 122500 | 49000 | | August | 300 | 125 | 90000 | 37500 | | September | 250 | 115 | 62500 | 28750 | | October | 150 | 80 | 22500 | 12000 | | Total | 2700 | 1150 | 660000 | 290000 | n = 10 Step 2: Calculate the slope (b) and y-intercept (a) using the least squares method. The formula for the slope (b) is: b = (n( xy) - ( x)( y))/(n( x^2) - ( x)^2) Substitute the values: b = (10(290000) - (2700)(1150))/(10(660000) - (2700)^2) b = (2900000 - 3105000)/(6600000 - 7290000) b = (-205000)/(-690000) ≈ 0.2971 The variable cost per unit (slope) is approximately 0.2971. The formula for the y-intercept (a) is: a = ( y - b( x))/(n) Substitute the values: a = (1150 - 0.2971(2700))/(10) a = (1150 - 802.17)/(10) a = (347.83)/(10) ≈ 34.783 The fixed cost (y-intercept) is approximately 34.78. Step 3: Determine the line of best fit. The line of best fit is represented by the equation y = a + bx, where y is the total overhead, a is the fixed cost, b is the variable cost per unit, and x is the number of units. y = 34.78 + 0.2971x Summary of results: i) High and Low Method: • Variable Cost Per Unit: 0.30 • Fixed Cost: 35 ii) Linear Regression Analysis: • Variable Cost Per Unit: 0.2971 • Fixed Cost: 34.78 • Line of Best Fit: y = 34.78 + 0.2971x Drop the next question.

Accepted Answer · 2026-08-25T15:45:58.133Z

Here's how to calculate the fixed and variable elements of the mixed factory overhead using the requested methods. i) The high and low method Step 1: Identify the high and low activity levels and their corresponding overhead costs. From the table: • Highest activity: July, 350 units, Overhead = 140 • Lowest activity: January and October, 150 units, Overhead = 80 Step 2: Calculate the variable cost per unit. The formula for variable cost per unit is: Variable Cost Per Unit = Highest Overhead Cost - Lowest Overhead CostHighest Activity Level - Lowest Activity Level Substitute the values: Variable Cost Per Unit = (140 - 80)/(350 - 150) = (60)/(200) = 0.30 The variable cost per unit is 0.30. Step 3: Calculate the total fixed cost. Total fixed cost can be found by taking the total cost at either the high or low activity level and subtracting the total variable cost at that level. Using the high activity level (July): Total Fixed Cost = Total Overhead at High Activity - (Variable Cost Per Unit × High Activity Level) Total Fixed Cost = 140 - (0.30 × 350) = 140 - 105 = 35 Using the low activity level (January/October): Total Fixed Cost = Total Overhead at Low Activity - (Variable Cost Per Unit × Low Activity Level) Total Fixed Cost = 80 - (0.30 × 150) = 80 - 45 = 35 The fixed cost is 35. ii) The linear regression analysis and determine the line of best fit Step 1: Set up the data for linear regression. We need the sum of x, y, xy, x^2, and the number of observations (n). | Month | Units (x) | Overhead (y) | x^2 | xy | | :-------- | :-------- | :----------- | :------ | :------ | | January | 150 | 80 | 22500 | 12000 | | February | 200 | 100 | 40000 | 20000 | | March | 300 | 135 | 90000 | 40500 | | April | 250 | 125 | 62500 | 31250 | | May | 300 | 130 | 90000 | 39000 | | June | 250 | 120 | 62500 | 30000 | | July | 350 | 140 | 122500 | 49000 | | August | 300 | 125 | 90000 | 37500 | | September | 250 | 115 | 62500 | 28750 | | October | 150 | 80 | 22500 | 12000 | | Total | 2700 | 1150 | 660000 | 290000 | n = 10 Step 2: Calculate the slope (b) and y-intercept (a) using the least squares method. The formula for the slope (b) is: b = (n( xy) - ( x)( y))/(n( x^2) - ( x)^2) Substitute the values: b = (10(290000) - (2700)(1150))/(10(660000) - (2700)^2) b = (2900000 - 3105000)/(6600000 - 7290000) b = (-205000)/(-690000) ≈ 0.2971 The variable cost per unit (slope) is approximately 0.2971. The formula for the y-intercept (a) is: a = ( y - b( x))/(n) Substitute the values: a = (1150 - 0.2971(2700))/(10) a = (1150 - 802.17)/(10) a = (347.83)/(10) ≈ 34.783 The fixed cost (y-intercept) is approximately 34.78. Step 3: Determine the line of best fit. The line of best fit is represented by the equation y = a + bx, where y is the total overhead, a is the fixed cost, b is the variable cost per unit, and x is the number of units. y = 34.78 + 0.2971x Summary of results: i) High and Low Method: • Variable Cost Per Unit: 0.30 • Fixed Cost: 35 ii) Linear Regression Analysis: • Variable Cost Per Unit: 0.2971 • Fixed Cost: 34.78 • Line of Best Fit: y = 34.78 + 0.2971x Drop the next question.

Calculate the fixed and variable elements of the above mixed factory overhead using: i. The high and low method; ii. The linear regression analysis and determine the line of best fit.

Need help with your own homework?

More Business/Management Questions

Calculate the fixed and variable elements of the above mixed factory overhead using: i. The high and low method; ii. The linear regression analysis and determine the line of best fit.

Need help with your own homework?

More Business/Management Questions