$1$: Use regression and show the equation used for Random to separate overhead into fixed and variable components. Please provide a step by step of this process

$2$: How much of the change in costs will this equation predict? Provide a step by step

$3$: What is the variable cost per unit for overhead? Round to the nearest cent Provide a step by step

$4$: Random analyzes their other costs and finds the following $($in addition to the overhead costs above$)$:

Direct Mat

Each unit of inventory uses $2$ gallons of materials and each gallon costs $$3$

Direct Labor

On average a worker can produce $16$ units of product in an $8$ hour shift and gets paid $$200$ for that shift $($how much per unit?$)$

Each month Random spends $$27,500$ on selling and administration costs

Sales price for $2023$ is estimated at $$38$ per unit

Please Provide a step by step

$5$: What is Random's contribution margin per unit? Round to the nearest cent Provide a step by step

$6$:How many units does Random need to sell in a month to break even in $2023?$ Provide a step by step

$7$:How many units does Random need to sell in a month to make $$20,000$ of profit before taxes? Provide a step by step

$8$: How much in dollars must Random sell in a month to make $$90,000$ in profit before taxes? Provide a step by step

$9$: Show the predicted contribution margin format income statement for January if production and sales are $7,100$ units for January $2023$

Show the predicted contribution margin format income statement for February $2023$ if sales increase from January by $200$ units.

Also in February, selling costs are increased by $$2,000/$month$,$ a new machine increases fixed overhead by $$6,000$

and makes it so that workers can make $24$ in a shift $($changes the direct labor per unit$)$

Other costs should be consistent with January.

Provide a step by step