Sebolt Wire Company heats copper ingots to very high temperatures by placing the ingots in a large heat coil. The heated ingots are then run through a shaping machine that shapes the soft ingot into wire. Due to the long heat-up time, the coil is never turned off. When an ingot is placed in the coil, the temperature is raised to an even higher level, and then the coil is allowed to drop to the “waiting” temperature between ingots. Management needs to know the variable cost of power involved in heating an ingot and the fixed cost of power during “waiting” periods. The following data on ingots processed and power costs are available:
Month Number of ingots Power cost
January 110 $5,500
February 90 $4,500
March 80 $4,400
April 100 $5,500
May 130 $6,000
June 120 $5,600
July 70 $4,000
August 60 $3,200
September 50 $3,400
October 40 $2,400
1. Using the high-low method, estimate a cost formula for power cost. Express the formula in the form Y = a + bX.
2. Prepare a scattergraph by plotting ingots processed and power cost on a graph. Draw a straight line though the two data points that correspond to the high and low levels of activity. Make sure your line intersects the Y-axis.
3. Comment on the accuracy of your high-low estimates assuming a least-squares regression analysis estimated the total fixed costs to be $1,185.45 per month and the variable cost to be $37.82 per ingot. How would the straight line that you drew in requirement 2 differ from a straight line that minimizes the sum of the squared errors?