Question

The Hard Rock Mining Company is developing cost formulas for management planning and decision-making purposes. The company's cost analyst has concluded that utilities cost is a mixed cost, and he is attempting to find a base that correlates with the cost. The controller has suggested that tons mined might be a good base to use in developing a cost formula. The production superintendent disagrees; she thinks that direct labor-hours would be a better base. The cost analyst has decided to try both bases and has assembled the following information: Direct Labor- Utilities Hours Cost Tons Mined Quarter Year 1: First Second Third Fourth Year 2: First Second Third Fourth 16,000 12,000 21,000 13,000 5,100 3,100 4,100 6,100 $ 51,000 $ 46,000 $ 61,000 $ 76,000 19,000 26,000 31,000 29,000 10,500 9,500 8,500 11,500 $ 105,000 $110,000 $ 86,000 $122,000 2-a. Using direct labor-hours as the independent variable, prepare a scattergraph that plots direct labor-hours on the horizontal axis and utilities cost on the vertical axis. Instructions: 1. On the graph below, use the point tool (Year 1-1st quarter) to plot direct labor-hours on the horizontal axis and utilities cost on the Vertical axis. 2. Repeat the same process for the plotter tools (Year 1-2nd quarter to Year 2-4th quarter). 3. To enter exact coordinates, click on the point and enter the values of x and y. 4. To remove a point from the graph, click on the point and select delete option. Year 1 - 1st quarter $140,000 o Year 1 - 2nd quarter $120,000 $100,000 Year 1 - 3rd quarter ies Cost $80,000 Year 1 - 4th quarter

Answer 1

Hard Rock Mining Company

2-(a) Scatter Graph

$140000 $120000 Year 2- 4th Quarter Year 2-2nd QuarterYear 2-1st Quarter $100000 Utilities Cost $80000 Year 2- 3rd Quarter Year 1-3rd Year 1- 4th Quarter Quarter Yeart-2nd Year 1-ist Quarter Quarter $40000 $20000 SO 0 2000 10000 12000 4000 6000 8000 Direct-Labor Cost-Hours

2-b

Least - Squares Regression method

Quarter Least-Squares Regression Method Direct Labor Hour Utilities Cost X Y X? XY 5100 3100 4100 6100 51000 46000 61000 76000 26010000 9610000 16810000 37210000 260100000 142600000 250100000 463600000 Year 1 First Second Third Fourth Year2 First Second Third Fourth Total 10500 9500 8500 11500 58400 105000 110000 86000 122000 657000 110250000 90250000 72250000 132250000 494640000 1102500000 1045000000 731000000 1403000000 5397900000

η = 8 ΣΧ = 58400 ΣΥ = 657000 ΣΧ2 = 494640000 Σ XY = 5397900000 nΣ ΧΥ – (Σ X)(ΣΥ) b = nΣ Χ’ - (Σ Χ) 8x5397900000 - 58400x657000 b 8x494640000 – (58400) 43183200000 – 38368800000 b 3957120000 – 3410560000 4814400000 b 546560000 b = 8.81 Π

ΣΥ - bΣ Χ a= n 657000-8.81x58400 a 8 657000 - 514504 a 8 142496 a 8 a = 17812 a=Total Fixed Utilities cost per quarter = $17812 b=Variable Utilities cost per direct labor-hour = $8.81 per labor-hour Y=a+bX Y=17812+8.81X