Problem Statement: An operations manager is trying to determine a production plan for the next week. There

are three products $($say$,$ P$,$ Q$,$ and Q$)$ to produce using four machines $($say$,$ A and B$,$ C$,$ and D$).$ Each of the four

machines performs a unique process. There is one machine of each type, and each machine is available for

$2400$ minutes per week. The unit processing times for each machine is given in Table $1.$

$$The unit revenues and maximum sales for the week are indicated in Table $2.$ Storage from one week to the next

is not permitted. The operating expenses associated with the plant are $$6000$ per week, regardless of how

many components and products are made. The $$6000$ includes all expenses except for material costs.

$1.$ Propose an LP model formulating this problem

hint use matrices and vector notations, to have a compact formulation