The administrator of Azalea Hills Hospital would like a cost formula linking the
ID: 2481253 • Letter: T
Question
The administrator of Azalea Hills Hospital would like a cost formula linking the costs involved in admitting patients to the number of patients admitting during a month. The admitting department's costs and the number of patients admitting during the immediately preceding eight months are given in the following table.
Month Number of Patients Admitted Admitting Department Costs
May 1,800 $14,700
June 1,900 15,200
July 1,700 13,700
August 1,600 14,000
September 1,500 14,300
October 1,300 13,100
November 1,100 12,800
December 1,500 14,600
1. Use the high-low method to establish the fixed and variable components of admitting costs.
2. Express the fixed and variable components of admitting costs as a cost formula in the linear equation form Y=a+bX.
Explanation / Answer
1) High Low Method:
Lowest level of activity - November - 1100 patients - $12,800
Highest level of activity - June - 1900 patients - $15,200
Variable cost = (cost at highest level - cost at lowest level)/(units at highest level - units at lowest level)
= (15200 - 12800)/(1900-1100) = $3 per patient
Fixed portion = 15200 - 3*1900 = $9,500
2) Linear equation:
month # patients costs X Y X*Y X*X may 1800 14700 26460000 3240000 jun 1900 15200 28880000 3610000 jul 1700 13700 23290000 2890000 aug 1600 14000 22400000 2560000 sep 1500 14300 21450000 2250000 oct 1300 13100 17030000 1690000 nov 1100 12800 14080000 1210000 dec 1500 14600 21900000 2250000 12400 112400 175490000 19700000 For y = a + bx Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)Intercept(a) = (Y - b(X)) / N b = (8*175490000 - 12400*112400)/(8*19700000-12400^2) = 2.6458 a = (112400 - 2.6458*12400)/8 = 9949 So the linear equation is Y = 9949 + 2.6548*X
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