LD company provides two cleaning services for staff uniforms to hotels and similar businesses. One of the services is a laundry service and the other is a dry cleaning service. Both of the services use the same resources, but in different quantities. Details of the expected resource requirements, revenues and costs of each service are shown below:
Selling price
Cleaning materials
Direct labour
Variable machine cost(3.00 per hour) Fixed costs
Profit
Laundry
# per service 5.60
2.00
1.20
0.50
1.15
0.75
Dry cleaning # per service 13.20
3.00
2.00 1.50 2.25 4.45
(#10.00 per ltr) (#6.00 per hour)
The annual fixed costs are #32,825
The maximum resources expected to be available
in December 2010 are:
Cleaning materials Direct labour hours Machine hours
5,000 litres 6,000 litres 5,000 hours
LD company has one particular contract which it entered into six months ago with a local hotel to guarantee 1,200 laundry services and 2,000 dry cleaning services every month. If LD
company does not honour this contract it has to pay substantial financial penalties to the local hotel.
The maximum demand for laundry is expected to be 14,000 services and for dry cleaning 9,975 services.
Required:
a) Assuming that a graphical lineal programming solution is to be used to maximize profit:
i. State the constraints and objective function
ii. Determine the maximum profit that can be made
b) Calculate the value of any slack and surplus and explain what they mean for LD company.
c) Calculate the shadow price of a machine hour and explain what this means for LD company.