A manufacturing company has an order for $500$ units of a product for delivery at the end of day $130.$ The

product consists of three components. Components B and C form the subassembly. Subassembly and

component A form the final assembly. Component A$,$ B and C are machined in the manufacturing shops A$,$

$B$ and $C$ of the company. No setup is required for the operations except the second operation of component

B$.$ This setup takes $4$ hours. Material is available for all parts. The following are the standard times for each

operation of a lot of $500$ units.

$($a$)$ Draw a backward schedule under the following conditions. When must components $A,B,$ and $C$ be

started to meet the delivery date?

Each operation of every component is processed by a different machine in the manufacturing shops.

All parts move in one lot of $500$ units.

$($b$)$ Suppose that the company wants to reduce the total manufacturing lead time as much as possible. For

that purpose, the company wants to use operations overlapping for one of the two components A and B$.$

Assume that the whole lot of $500$ units is divided into two sublots. Which component should be selected?

What should be the size of each sublot? What will be the new total manufacturing lead time?

$($c$)$ Suppose that the company wants to reduce the total manufacturing lead time as much as possible. For

that purpose, the company wants to use operations splitting for the first operation of either component A

or component B$,$ using one extra machine. Which component should be selected? What will be the new

total manufacturing lead time?