Question

Matt owns a machine shop. In reviewing the shop's utility bills for the past 12 months, he found that the highest bill of $2, 700 occurred in August when the worked 1, 300 machine hours. The lowest utility bill of $2, 500 occurred in December when the machines worked 800 machine hours. 1. Calculate the variable rate per machine hour and the total fixed utility cost. 2. Show the equation for determining total utility cost for the machine shop. 3. If Matt anticipates using 1, 200 machine hours in January, predict the shop's total utility bill using the equation from Requirement 2. Calculate the variable rate per machine hour and the total fixed utility cost. First, calculate the variable rate per machine hour. Select the formula labels, then enter the amounts and compute the variable rate per machine hour. (Use the high-low method. Round your answer to the nearest cent.)/= variable rate per machine hour/= Calculate the total fixed cost. Select the formula labels, then enter the amounts and compute the total fixed cost. (Use the highest point.) - = Total fixed cost + = Show the equation for determining total utility cost for the machine shop. (times) + = Total utility cost. If Matt anticipates using 1, 200 machine hours in January predict the shop's total utility bill using the equation form Requirement 2.

Answer 1

Answer:

The variable rate is 0.4 $/machine-hour.

The equation fot the utility bill is $C(M)=0.4*M+2180$.

If Matt anticipates using 1200 machine hours in January, his utility bill will be $ 2660.

Explanation:

We have two points in the year that will let us calculate the fixed utility cost and the variable utility cost.

We will end up with a equation of a line, like this

$C(M)=v*M+F$

Where C (M) is the total utility cost, v is the variable utility cost per machine hour, M are the machines running hours and F is the fixed utility cost.

We have two unknowns and two equations, so it can be solved.

First we can substract the two bills (the highest and the lowest) and equal that to the equation of the line we described

$(2700-2500)=C(1300)-C(800)=(v*1300+F)-(v*800+F)\\\\200=v*1300+F-v*800-F=500*v\\\\v=200/500=0.4$

The variable rate is 0.4 $/machine-hour.

Then we can replace v in one of the equations

$2500=C(800)=0.4*800+F\\\\2500=320+F\\\\F=2500-320=2180$

The fixed utility cost are 2180 $/month.

The equation fot the utility bill is $C(M)=0.4*M+2180$.

If Matt anticipates using 1200 machine hours in January, his utility bill will be $ 2660.

$C(1200)=0.4*1200+2180=480+2180=2660$