Random Inc. Cost data for the last 3 years Overhead Costs Units Produced January-20 February-20 March-20 April-20 May-20 June-20 July-20 August-20 September-20 October-20 November-20 December-20 January-21 February-21 March-21 April-21 May-21 June-21 July-21 August-21 September-21 October-21 November-21 December-21 January-22 February-22 March-22 April-22 May-22 June-22 July-22 August-22 September-22 October-22 November-22 December-22 $78,000 $91,000 $100,000 5,679 $78,000 $89,000 \begin{tabular}{rr} $93,000 & 7,630 \\ \hline$87,000 & 6,331 \\ \hline \end{tabular} $87,000 $94,000 $85,000 $104,500 $92,000 $92,000 $104,000 \begin{tabular}{rr} $99,000 & 9,062 \\ \hline$77,000 & 5,410 \end{tabular} $77,000 $83,000 5,410 $95,000 6,556 7,850 $92,000 $77,000 $105,000 $103,000 $96,000 $100,000 $83,000 $7,000 $74,000 $81,000 $82,000 $82,000 $72,000 $73,00 $73,000 $82,000 Use regression and show the equation used for Random to separate overhead into fixed and variable components. How much of the change in costs will this equation predict? What is the variable cost per unit for overhead? Round to the nearest cent What is the fixed overhead cost per month? Round to the nearest dollar 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 What is Random's contribution margin per unit? Round to the nearest cent How many units does Random need to sell in a month to break even in 2023 ? How many units does Random need to sell in a month to make $20,000 of profit before taxes? How much in dollars must Random sell in a month to make $90,000 in profit before taxes? 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