QP (Pty) Ltd is a food processing company that produces pre-prepared meals for sale to the Army Support Base Western Cape (ASB WC) that it supplies to different units for deployment purposes, as well as other food supply companies.  The company specialises in three particular pre-prepared meals and has invested significantly in modern manufacturing processes to ensure a high quality product.  The company is very aware of the importance of training and retaining high quality staff in all areas of the company.  In order to ensure their production employees’ commitment to the company, the employees are guaranteed a weekly salary that is equivalent to their normal working hours paid at their normal hourly rate of R7 per hour.

The meals are produced in batches of 100 units.  Costs and selling prices per batch are as follows:

Meal	TR	PN	BE
	R/batch	R/batch	R/batch
Selling price	600	500	400
Ingredient K (R5/kg)	150	120	90
Ingredient L (R10/kg)	70	90	40
Ingredient M (R15/kg)	30	75	45
Labour (R7/hour)	21	28	42
Factory costs absorbed	20	80	40

QP (Pty) Ltd is preparing its production plans for the next three months and has estimated the maximum demand from its customers to be as follows:

            TR       500 batches

            PN       400 batches

            BE       350 batches

These demand maximums are amended figures because the ASB has just delayed its request for a large order and QP unusually has some spare capacity over the next three months.  However, these demand maximums do include a contract for the delivery of 50 batches of each to an important customer.  If this minimum contract is not satisfied then QP (Pty) Ltd will have to pay a substantial financial penalty for non-delivery.

The production director is concerned at hearing news that two of the ingredients used are expected to be in short supply for the next three months.  QP (Pty) Ltd does not hold inventory of these ingredients and although there are no supply problems for ingredient K, the supplies of ingredients L and M are expected to be limited to:

            Ingredient L     7 000 kilograms

            Ingredient M    3 000 kilograms

The production director has researched the problem and found that ingredient V can be used as a direct substitute for ingredient M.  It also costs the same as ingredient M.  There is an unlimited supply of ingredient V.

Required:

Prepare calculations to determine the production mix that will maximise the profit of QP (Pty) Ltd during the next three months.