Question

Cost estimation – utilities The Karmichaels’ property has single connections and metres for gas and water. The following information is provided regarding these utilities for the past year.

1.Using the high-low method, determine the liner cost function for both the gas and water costs.

2.Express the combined costs in a single linear cost equation.

3.Write an explanation of the procedure and the information it produces, as well as how this information is useful for cost management, to the Karmichaels.

	Gas		Water
	Units	Cost $	Units	Cost $
January	375	$   343.75	3,500	$ 1,530.00
February	425	$   356.25	3,750	$ 1,612.50
March	550	$   387.50	2,250	$ 1,117.50
April	350	$   337.50	2,000	$ 1,035.00
May	345	$   336.25	1,800	$    969.00
June	420	$   355.00	2,100	$ 1,068.00
July	425	$   356.25	2,750	$ 1,282.50
August	476	$   369.00	2,615	$ 1,237.95
September	510	$   377.50	2,800	$ 1,299.00
October	445	$   361.25	2,975	$ 1,356.75
November	375	$   343.75	3,100	$ 1,398.00
December	315	$   328.75	3,255	$ 1,449.15

Answer 1

	Gas		Water
	Units	Cost $	Units	Cost $
January	375	$   343.75	3500	$ 1,530.00
February	425	$   356.25	3750	$ 1,612.50
March	550	$   387.50	2250	$ 1,117.50
April	350	$   337.50	2000	$ 1,035.00
May	345	$   336.25	1800	$    969.00
June	420	$   355.00	2100	$ 1,068.00
July	425	$   356.25	2750	$ 1,282.50
August	476	$   369.00	2615	$ 1,237.95
September	510	$   377.50	2800	$ 1,299.00
October	445	$   361.25	2975	$ 1,356.75
November	375	$   343.75	3100	$ 1,398.00
December	315	$   328.75	3255	$ 1,449.15
Variable cost = (Total cost of high activity – Total cost low activity) / (Highest activity unit – Lowest activity unit)
Highest Activity	550	$   387.50	3750	$ 1,612.50
Lowest Activity	315	$   328.75	1800	$    969.00
Variable Cost per unit	(378.50-328.75)/(550-315)		(1612.50-969)/(3750-1800)
	0.21		0.33
Fixed Cost
Total cost = (Variable cost per unit x Units produced) + Total fixed cost
387.50 = (.21*550 units)+ Fixed Cost			1612.50= (.33* 3750 unis +Fixed Cost
387.50 = 116.43 + Fixed Cost			1612.50 = 1237.50 + Fixed Cost
Therefore, Fixed Cost = 387.50-116.43			Therefore, Fixed Cost = 1612.50-1237.50
Total Fixed Cost = 271.06			Total Fixed Cost = 375
Total Cost Equation
(Variable cost per unit * units) + Fixed Cost
(.21*X) + 271.06			(.33*X) + 375