How much of each fuel should be product in order to maximize profit?

Question

A chemical company make two different fuel , Y each of which is different mixture of three chemicals A; B; and C, the amounts of A,B, and C available are:

A: 100tonnes

B: 400tonnes

C: 420tonnes

Fuel X uses 6tonnes of material C and 4tonnes of material B, while fuel Y use 3tonnes of A 5tonnes of B, and 2 of C: A 10-ton unit of fuel X yields a profit of $1000, while a similar unit of fuel Y gives a profit of $2500.

Answer 1

Hi Sopheak! Looks like 4B+6C yields $1000 ... 3A+5B+2C yields $2500 ... two simple choices are to use up A in the hi-profit fuel Y or make as much fuel X as possible:

Max Y -- 33 units makes $82K using up all A, leaving 235B and 354C for 58 units of X at $58K, $140K total.

Max X -- 70 units makes only $70K using up all C ...

Check the "Max Y" by trimming back to make more X: only 30 units Y makes $7500 LESS, freeing up 15B+6C with remainder 3B+6C to make 2 more X at $2000 MORE -- bad trade: make Max Y ... Regards :)

Answer 2

Hi Sopheak! Looks like 4B+6C yields $1000 ... 3A+5B+2C yields $2500 ... two simple choices are to use up A in the hi-profit fuel Y or make as much fuel X as possible:

Max Y -- 33 units makes $82K using up all A, leaving 235B and 354C for 58 units of X at $58K, $140K total.

Max X -- 70 units makes only $70K using up all C ...

Check the "Max Y" by trimming back to make more X: only 30 units Y makes $7500 LESS, freeing up 15B+6C with remainder 3B+6C to make 2 more X at $2000 MORE -- bad trade: make Max Y ... Regards :)