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Michael Products, Inc. has decided to introduce a new product, which can be manufactured by either a computer$-$assisted manufacturing system or a labor$-$intensive production system. The manufacturing method will not affect the quality of the product. The estimated manufacturing costs by the two methods are as follows:

Computer$-$Assisted Manufacturing System Labor$-$Intensive Production System

Direct Material $$5\mathrm{.}00$ $$7\mathrm{.}00$

Direct Labor $($DLH denotes direct$-$labor hours$)0\mathrm{.}5$DLH@$$18$ $$9\mathrm{.}001\mathrm{.}1$DLH@$$14$ $$15\mathrm{.}40$

Variable mfg$.$ overhead $($applied based on DLH$)0\mathrm{.}5$DLH@$$10$ $$5\mathrm{.}001\mathrm{.}1$DLH@$$10$ $$11\mathrm{.}00$

Fixed mfg$.$ overhead$*$ $$3,250,000$ $$150,000$

$*$ These costs are directly traceable to the new product line and they would not be incurred if the new product were not produced.

The company's market research department has recommended an introductory unit sales price of $$60\mathrm{.}00.$ Selling expenses are estimated as $$600,000$ annually plus $$1\mathrm{.}80$ for each unit sold.

Required: $($Round up all numbers to the next higher digit in case of breakeven volumes and round up to the nearest integer in other cases.$)$

a$)$ Calculate the estimated break$-$even point $($in annual sales volume in units$)$ of the new product if the compnay uses the $($i$)$ Computer$-$Assisted Manufacturing System; $($ii$)$ Labor$-$Intensive Production System.

b$)$Estimate the number of units that Michael Products should sell to earn an after$-$tax profit of $$4\mathrm{.}20$ million under $($i$)$ Computer$-$Assisted Manufacturing System $($ii$)$ Labor$-$Intensive Production System. Assume an income$-$tax rate of $40\%$

c$)$ Determine the annual sales volume $($in units$)$ at which the firm would be indifferent $($if profit $(4$ points$)$ maximization is the objective$)$ between choosing between the two manufacturing methods. Justify your answer with appropriate calculations.

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