Profit Math Problum. Please Help!

[desi43]

Can someone help? If anyone can help to let me know if I did the problem correctly and if not, help me to figure it out I would really appreciate it. thanks!



Q: a popcorn company makes butter flavored popcorn and cheese flavored popcorn.

there are 3 stages of production: popping, flavoring and packing.

each kilogram of butter popcorn takes 3 mins to pop, 4mins to flavor and 1 min to pack. each kilogram of cheese takes 3 mins to pop, 6 mins to flavor and 2 mins to pack.

the net profit on each kilogram of butter is $0.18 and $0.28 for cheese.

popping is done 4hrs each day flavoring is done 7 hrs each day and the packer is available 2 hrs each day. How many kilograms of popcorn must the company produce to maximize their net profit?


A: i got these constraints from the word problum.

3x+3y< 240
4x+6y < 420
x+2y< 120

P= 0.18X+0.28Y


after i graphed it i got (40,40) as a maximun point. then used it in P= 0.18X+0.28Y to get 18.4 = 19 kilograms


is this right? please help! also i got (40,40) by looking at the graph , so if that is wrong please let me know. thanks again.

 

[Gene]

Your equations are good but I would STRONGLY suggest that you use variables that point to what they stand for. b for buttered instead of x and c for cheese instead of y.
Also X is a different variable than x. Don't mix them if they are the same.
Finaly there are four points to consider from the graph.
(0,0), (0,60), (40,40) and (80,0). You must check each for max profit.
(0,0) isn't likely. You should make something but it is a solution point. Each of the other three have to be checked in the profit equation. Perhaps you want to make all of one kind and drop the other. You don't know till you check.
Profit is in dollars, not kilograms. x and y are in kilos
.18 * 40kg + .28 * 40kg = $18.40 so despite my nitpicking you got it right.