Using the simplex procedure, solve the spare$-$parts manufacturer's problem below:

A small firm specializes in making five types of spare automobile parts. Each

part is first cast from iron in the casting shop and then sent to the finishing shop

where holes are drilled, surfaces are turned, and edges are ground. The required

worker$-$hours $($per $100$ units$)$ for each of the parts of the two shops are shown

below:

The profits from the parts are $$30,$$$20,$$$40,$$$25,$ and $$10($per $100$ units$),$ re$-$

spectively. The capacities of the casting and finishing shops over the next month

are $700$ and $1000$ worker$-$hours, respectively. Formulate the problem of deter$-$

mining the quantities of each spare part to be made during the month so as to

maximize profit.