Linear Programming

Dear Mr Moffat,

Below question from exam kit that I went through which I have doubts and difficulties to understand the answers provided. Could you kindly help, please?

Questions

LD Co 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 cost of each service are shown below:

Laundry Dry Cleaning
$ per service $ per services

Selling price 5.6 13.20
Cleaning Material ($10.00 per litre) 2.00 3.00
Direct Labour ($6.00 per hour) 1.2 2.00
Variable machine cost ($3.00 per hour) 0.5 1.5
Fixed cost 1.15 2.25
Profit 0.75 4.45
Total annual fixed costs are $32.825

The maximum resources expected to be available in December 20×3 are
Cleaning material 5000 litres
Direct labour hours 6000 hours
Machine hours 5000 hours
LD Co has one particular contract which it entered into six months ago with a local hotel to guarantee 1200 laundry services and 2000 dry cleaning services every month. If LD Co 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 14000 services and for dry cleaning 9975 services.
Required:

a) Assuming that a graphical linear programming solution is to be used to maximise profit:
i) State the constraints and objective functions
II) Determine the maximum profit that can be made.

Part I) no problems.
Part II) I don t fully understand how the ISO contribution line has been calculated.
C= 1.9L+6.7D
If C = (1.9X6.7*1000)=12.730 then
if L 6.700, D=0
if D = 1900

Optimal solution

L=1200 and 0.167L +0,5D=5000
If L 1200, then D (5000-200) x2=9600
Optimal solution is to carry out 1200 laundry services and 9600 dry cleaning services

I don t understand where 9600 came from.
Is there another approach that I have use that might make more sense to me?
I did not understand why they use the minimum guarantee to calculate the optimal solution. And why 1200 instead of 2000.

Apologies for the long question and I hope it is not too much confusing.

Thanks in advance

Gabbi