Forward and Foundry Ltd$.$ is feeling the effects of a general recession in the industry. Its budget for the coming half year is based on an output of only $500$ tons of casting a month which is less than half of its capacity. The prices of casting vary with the composition of the metal and the shape of the mould, but they average $`175$ a ton. The following details are from the Monthly Production Cost Budget at $500$ tone levels:

Core Making

Melting and Pouring

Moulding

Cleaning and Grinding

$`$

$`$

$`$

$`$

Labour

$10,000$

$16,000$

$6,000$

$4,500$

Variable overheads

$3,000$

$1,000$

$1,000$

$1,000$

Fixed overhead

$5,000$

$9,000$

$2,000$

$1,000$

$18,000$

$26,000$

$9,000$

$6,500$

Labour and O$.$H rate per direct labour hour

$9\mathrm{.}00$

$6\mathrm{.}50$

$6\mathrm{.}00$

$5\mathrm{.}2$

Operation at this level has brought the company to the brink of break$-$even. It is feared that if the lack of work continues, the company may have to lay off some of the most highly skilled workers whom it would be difficult to get back when the volume picks up later on$.$ No wonder, the work$$s Manager at this Juncture, welcomes an order for $90,000$ casting, each weighing about $40$ lbs$.,$ to be delivered on a regular schedule during the next six months. As the immediate concern of the Works Manager is to keep his work force occupied, he does not want to lose the order and is ready to recommended a quotation on a no$-$profit and no$-$loss basis.

Materials required would cost $`1$ per casting after deducting scrap credits. The direct labour hour per casting required for each department would be:

Core Making

$0\mathrm{.}09$

Melting and pouring

$0\mathrm{.}15$

Moulding

$0\mathrm{.}06$

Cleaning and Grinding

$0\mathrm{.}06$

Variable overheads would bear a normal relationship to labour cost in the melting and pouring department and in the moulding department. In core making, cleaning and grinding however, the extra labour requirements would not be accompanied by proportionate increases in variable overhead. Variable overhead would increase by $`1\mathrm{.}20$ for every additional labour hour in core making and by $30$ paise for every additional labour hour in cleaning and grinding. Standard wage rates are in operation in each department and no labour variances are anticipated. To handle an order as large as this, certain increases in factory overheads would be necessary amounting to $`1,000$ a month for all departments put together. Production for this order would be spread evenly over the six months period. You are required to:

$($a$)$ Prepare a revised monthly labour and overhead cost budget, reflecting the addition of this order.

$($b$)$ Determine the lowest price at which quotation can be given for $90,000$ castings without incurring a loss.