KYZ Ltd manufactures and distributes 2 products, Z1 and Z2. Each product utilises the same direct materials and direct labour resources. Unit revenue and variable cost details are shown below.

KYZ Ltd – Unit Revenue and Contribution Data

Product:	Z1		Z2
	£	£	£	£
Selling price		20.00		40.00
Direct materials (at £2 per kilo)	5.00		2.00
Direct labour (at £10 per hour)	10.00	(15.00)	30.00	(32.00)
Unit contribution:		5.00		8.00

Maximum monthly demand is for 300 units of each product per month.

The production manager of KYZ Ltd has advised you that, for next month, only 500 kilos of direct materials and 950 direct labour hours are available to the company for production.

Note: No inventories of direct materials or finished goods are held and it is the short-term objective of KYZ Ltd to always maximise total contribution.

Required:

1. Calculate the maximum contribution achievable where no production constraints exist                                                                               

2. State the objective function and, in the light of the materials, labour and demand constraints construct a linear programming model in algebraic form

                

3. Using your linear programming model, establish the product mix that will maximise contribution and evaluate the contribution lost because of the resource shortages   

4. Explain the term “shadow pricing” and briefly explain how shadow price calculations may inform management planning decision-making

Number values / calculations are not required