$($a$)R$&$K$ Industries manufactures and sells packing machinery for which a particular type

of material is needed. The machinery is of two types: Ordinary and Automatic, the cost

details of which are given below:

Total fixed overhead Rs $10,000$

When the total availability of raw materials is $4,000kg$ and maximum sales potential of

each product is $1,000$ units, find the product mix to yield maximum profit.

$[10$ marks$]$

$($b$)$ A company estimates its sales as Rs $45,000$ for the first $6$ months and Rs $50,000$ during

the next six months in a financial year. Its estimated total costs are Rs $40,000$ and

Rs $43,000$ respectively for the two periods.

Required:

At what sales volume does this company break$-$even, assuming that the fixed costs are

equal for both the periods.