Tasha & Tisha Ltd $($T&T$)$ is a company that specialises in online t$-$shirt selling. The company's unique selling point is its innovative and open design system. Anyone in the world can submit a design and if it is popular enough $($i$.$e$.,$ gets enough votes$),$ T&T will produce and market the t$-$shirt on its well$-$known website. The designer of each $t-$shirt is guaranteed a fixed percentage of each sale in return for their successful design work. Each t$-$shirt sells for K$300.$ Designers get K$50$ from the sale of each t$-$shirt that they have designed. The website is so popular that the company's most successful t$-$shirt designers are able to make a living just by creating new designs for T&T$.$ The company expects to produce and sell $100,000t-$shirts this year, although there is $$ total production capacity of $110,000$ in the current factory setup. Fixed costs are K$4,000,000$ per year. The direct costs of production are K$245\mathrm{.}00$ per t$-$shirt $($this includes K$50$ paid to the designers, the purchase o: 'unfinished' t$-$shirts from a Chinese supplier, factory floor staff, dies, paints, postage, etc.$).$

Oliver Chisha, the Operations Manager, is examining a proposal put forward by the company's CEO to buy in a new automated screen$-$printing machine that links with new design software. This would enable a new design and manufacturing process capable of producing very large runs of custom designs. The quality would also greatly improve. Production capacity could be increased to $200,000$ t$-$shirts per year. There are very large overheads associated with the purchase of the new machine and IT system, especially the high cost of financing these purchases. Total fixed costs would double to K$8,000,000$ per year. Savings would be made by reducing the number of factory workers directly employed in the manufacturing process. Some of these savings would then be used to purchase in higher priced and higher quality unfinished t$-$shirts. Direct costs of production would decrease to K$175\mathrm{.}00$ per t$-$shirt. Research from the marketing department indicates that higher quality t$-$shirts, higher quality designs and a price reduction to K$250$ would increase the demand for T&T by $50$ per cent to $150,000$ t$-$shirts per year.

Required:

$($a$)$ Construct a break$-$even graph $($use of e$-$graphs is allowed$)$ to represent the current data, identifying the break$-$even level of production and the margin of margin

$($b$)$ Management has decided that the return on capital employed should be at least $15\%.$ In the case of current figures, the net profit would need to be at least K$2,000,000$ to achieve this. Calculate the output needed if a profit target of $K2,000,000$ is included

$($c$)$ Calculate the following:

The break$-$even level of output associated with the new production system

The margin of safety associated with the new production system

The profit associated with the current system of production

The profit associated with the new production system

$($d$)$ Based on financial and non$-$financial factors, advise the firm as to whether it should remain as it is or to adopt the new design and production system. You should include an evaluation of the advantages and limitations of break$-$even analysis in your answer.