DCF techniques – linear programming

Hi Sir,

Following the example in your lecture on DCF linear programming where the amount of deposit at Time 0 is subject to the constraint of P >=0 , for completeness shouldn’t P also be constrained to P<= $14,000? As it is technically possible to not invest in any of the a, b or c projects at Time 0, and earning a deposit interest of 7% on the deposit (despite the loss due to the 10% cost of capital) in order to have more funds available Time 1? I am aware it doesn’t make commercial sense but mathematically this seems to satisfy all the constraints?

And perhaps it might be worthwhile if the investment capital required at Time 1 for the projects were much more than those illustrated in the example?

Thanks in advance for your guidance.

Regards,
Tim