Michael owns a machine shop. In reviewing the shop's utility bills for the past $12$ months, he found that the highest bill of $$2,400$ occurred in August when the machine worked $1,000$ machine hours. The lowest utility bill of $$2,200$ occurred in December when the machines worked $500$ machine hours. $1.$ Use the high$-$low method to calculate the variable cost per machine hour and

the total fixed utility cost.

$2.$ Show the equation for determining the total utility cost for the machine shop.

$3.$ If Michael anticipates using $700$ machine hours in January, predict the shop's

total utility bill using the equation from Requirement $2.$