Problem $11\mathrm{.}1$

An umbrella manufacturer makes an average profit of $2\mathrm{.}50$ per unit on a selling price of $14\mathrm{.}30$ by producing and selling $60,000$ units at $60$ per cent of potential capacity.

His cost of sales per unit is as follows :

Direct materials

Direct wages

Factory overhead

Sales overhead

$3\mathrm{.}50$

$1\mathrm{.}25$

$6\mathrm{.}25(50\%$ fixed$)$

Re$.0\mathrm{.}80(25\%$ variable$)$

During the current year, he intends to produce the same number but estimates that his fixed cost would go up by $10$ per cent while the rates of direct wages and direct materials will increase by $8\%$ and $6\%$ respectively, However, the selling price cannot be changed.

Under this situation, he obtains an offer for a further $20\%$ of his potential capacity.

What minimum price would you recommend for acceptance of the offer to ensure the manufacturer and overall profit of $1,67,300?$