B The Manager of a Process Plant has requested you to assist him in improving

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the economic performance of the facility. He has found that he is not meeting the full market demand and wishes to configure his production facility so as to maximise the throughput of the firm.

The production operation has four resources: A$,$ B$,$ C$,$ and D each manned by one operator. Each of these resources has $2400$ minutes of operating time available per week from $8am$ to $4pm$ per day and can be used on only one operation at a time. There are three products, P$,$ Q and R$.$ Product P sells for $90$ per unit and has a maximum demand of $100$ units per week. Product $Q$ sells for $100$ per unit and has a maximum demand of $100$ units per week. Product R sells for $80$ per unit and has a maximum demand of $70$ units per week. The operating expense for the entire facility is $8,000$ per week, exclusive of material costs. $85,000$ of capital resources and raw materials are maintained in stock at all times.

The products require production time on the resources and raw materials according to the process flow chart shown on Figure Q$4.$

Raw Material $1$ is purchased for $10$ per unit, Raw Material $2$ costs $25$ per unit, and Raw Material $3$ costs $20$ per unit.

Producing a unit of Product $P$ requires one unit of Raw Material $1,$ processed on at Resource A for $15$ minutes, then by Resource $C$ for $10$ minutes. It also requires one unit of Material $2,$ processed on at Resource B for $15$ minutes, then at Resource $C$ for $5$ minutes. One each of these parts is then assembled together with Purchased Part PP$1$ at Resource D in an operation that takes $15$ minutes, after which it is ready for sale as Product $P.$

Producing a unit of Product $Q$ requires one unit of Raw Material $2,$ processed on Resource B for $15$ minutes, then at $C$ for $5$ minutes. It also requires one unit of Raw Material $3,$ processed on at Resource A for $10$ minutes and then at Resource $B$ for $15$ minutes. Then one unit of the part from $C$ and one unit of the part from B are assembled together at Resource D in an operation that takes $5$ minutes, after which it is ready for sale as Product $Q.$

Producing a unit of Product $R$ requires one unit of Raw Material $3,$ and can be processed on resource $B(5$mins or on resource A $(15$mins$).$ The relevant process engineer recommends using resource $B$ instead of resource A since it only takes a third of the time.

How many units of $P,Q$ and $R($if any$)$ should be produced in order to maximise the economic performance of this facility? Compute the expected Key Performance Indicators $($KPIs$).$ Provide a full rationale for your answer.