Linear Programming

Hi Mr. Maffot

I need help solving this question. The first part of the question i completely understand. Its the second part i need help with.
Please explain the second part of the question for me. How do i find the constraints?

Q.) W plc 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:

Laundry Dry cleaning
$ per service $ per service
Selling price 7.00 12.00
Cleaning materials ($10.00 per litre) 2.00 3.00
Direct labour ($6.00 per hour) 1.20 2.00
Variable machine cost ($3.00 per hour) 0.50 1.50
Fixed costs * 1.15 2.25
Profit 2.15 3.25

* The fixed costs per service were based on meeting the budget demand for December 2003.
W plc has already prepared its budget for December based on sales and operational activities of
8,000 laundry services and 10,500 dry cleaning services. but it is now revising its plans because of
forecast resource problems.
The maximum resources expected to be available in December 2003 are:
Cleaning materials 5,000 litres
Direct labour hours 6,000 hours
Machine hours 5,000 hours
W plc 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 W plc does not
honour this contract it has to pay substantial financial penalties to the local hotel.
Required:
(a) Calculate the mix of services that should be provided by W plc so as to maximise its profit
for December 2003.
(9 marks)
(b) The Sales Director has reviewed the selling prices being used by W plc and has provided
the following further information:
? if the price for laundry were to be reduced to $5.60 per service, this would increase
the demand to 14,000 services;
? if the price for dry cleaning were to be increased to $13.20 per service, this would
reduce the demand to 9,975 services.
Required:
Assuming that such selling price changes would apply to all sales and that the resource limitations
continue to apply, and that a graphical linear programming solution is to be used to maximise
profit.
(i) state the constraints and objective function; (6 marks)
(ii) use a graphical linear programming solution to advise W plc whether it should revise its
selling prices.