Case StudyIt's nice to have supply options, but I$\text{'}$m going bananas trying to sort out these slit steel bids, exclaimed Christopher Lane, purchasing manager for Sarbec Ltd$.$"I see what you mean", responded Jack Martin, Lane's assistant. Let me call my friend over in the accounting office. He'll have some suggestions for us$.$'Sarbec Ltd needs a total of $125$ tonnes of sheet steel$50$ tonnes of $4$ centimetre width and $75$ tonnes of $8$ centimetre width for a customer's job. Sarbec can purchase the sheet steel in these widths directly from Jensteel Ltd$,$ a steel manufacturer, or it can purchase sheet steel from Jensteel that is $48$ centimetres wide and then have it slit into the desired widths by Precut Pty Ltd$.$ both vendors are local and have previously supplied materials to Sarbec.Precut specialises in slitting sheet steel, provided by a customer, into any desired width. When negotiating a contract, Precut tells its customers that there is a scrap loss in the slitting operation, but that this loss has never exceeded $2\mathrm{.}5$ per cent of input tonnes. Precut recommends that if a customer has a specific tonnage requirement, it should supply an adequate amount of steel to yield the desired quantity. Precut's charges for steel slitting are based on good output, not input handled.The $48-$centimetre sheet steel is a regular stock item of Jensteel and can be shipped to Precut within five days of receipt of Sarbec's purchase order. If Jensteel is to do the slitting, shipment to Sarbec would be scheduled for $15$ days from receipt of the order. Precut has quoted delivery at $10$ days after receipt of the sheet steel. In prior dealings, Sarbec has found both Jensteel and Precut to be reliable vendors with high quality products.Sarbec has received the following price quotations from Jensteel and Precut: In addition to the above information, Precut has informed Sarbec that if Sarbec purchases $100$ output tonnes of each width, the per$-$tonne slitting rates would be reduced by $12$ per cent.Sarbec knows that the same customer will be placing a new order in the near future for the same material and estimates it would have to store the additional tonnage for an average of two months at a carrying cost of $$1\mathrm{.}50$ per month for each tonne. There would be no change in Jensteel's prices for additional tonnes delivered to Precut.As Martin's friend in the accounting office, you have just received a phone call for help.