$($a$)$ A space explorer on a distant moon finds an alien supply base. The explorer has a high$-$tech container that can hold a maximum of $120$ kgs $.$ The materials and their respective weights and values are:

$-$Xenonite: $40kgs,$$$6000$

$-$Zaltron Crystals: $30kgs,$$$3000$

Omega Fluid: $20kgs,$$$4000$

Quantum Dust: $25kgs,$$$3500$

Photon Ore: $35kgs,$$$1500$

Plasma Fibers: $50kgs,$$$2000$

Use the fractional knapsack algorithm to decide how much of each material should be collected to maximize earnings. Show your solution step$-$bystep.

b$)$ What would be the solution if only whole units of each material could be collected?

$[4+4$ Marks$]$