$($b$)$ Supreme Ceramics Limited manufactures product $x$ whose selling price is Rs$.10$ per unit. The firm has the capacity to produce $10,000$ units. The variable costs are Rs$.2\mathrm{.}50$ per unit. Fixed costs are estimated at Rs$.30,000$ upto the capacity utilization level of $50\%,$ Rs$.36,000$ above that level but Rs$.42,000$ if the level of capacity utilization is $80\%$ & above.

$($i$)$ What is break$-$even point?

$($ii$)$ What will be the operating profits of the firm, if the levels of capacity utilizationtare $70\%,80\%$ and $90\%$ respectively?

$($iii$)$ What is the level of activity at which the firm can make an operating profit of Rs$.18,000?$

$($iv$)$ Management of the firm is advised that, if the selling price is reduced to Rs$.9$ per unit, sales will go up from $7,000$ units to $7\mathrm{.}500$ units. Is it worthwhile to reduce the selling price?