Write a linear cost function equation for each of the following conditions. Use y for estimated costs and X for activity of the cost driver.

a. Direct manufacturing labor is $10 per hour.

b. Direct materials cost $15.60 per cubic yard.

c. Utilities have a minimum charge of $5,000, plus a charge of $0.30 per kilowatt-hour.

d. Machine operating costs include $300,000 of machine depreciation per year, plus $100 of utility costs for each day the machinery is in operation.

a)

y = $10x

b)

y = $15.6x

c)

y = $5000 + $0.3x

d)

y = $300000 + $100x

Explanation:

y for estimated costs and X for activity of the cost driver. Linear cost function is given as:

y = a + bx.

Where y is the cost being predicted, x is the cost driver, a is the fixed cost (intercept) and b is the variable cost per unit (slope)

a) Since Direct manufacturing labor is $10 per hour, variable cost (b) = Direct manufacturing labor = $10

Therefore:

y = $10x

b) variable cost (b) = Direct materials cost = $15.60 per cubic yard.

Therefore:

y = $15.6x

c) Fixed cost (a) = utilities = $5000 and variable cost (b) = charges = $0.3 per kilowatt-hour. Therefore:

y = $5000 + $0.3x

d) Fixed cost (a) = Machine operating costs = $300000 and variable cost (b) = utility costs = $100 per day. Therefore:

y = $300000 + $100x