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Hmmm found one more invitation 😉 But I am gonna make this more challenging 😉 First person to PM me the answer gets an invitation.

PLEASE DO NOT PM ME IF YOU ALREADY HAVE A GMAIL ACCOUNT!

Question:

A cereal company makes cereals from several ingredients (oats and rice). These ingredients have Vitamins A and B in them. Each box of cereal needs to have 48 miligrams of Vitamin A and 12 miligrams of Vitamin B, while minimizing cost. An ounce of oat contributes 8 mg of Vitamin A and 1 mg of Vitamin B whereas an ounce of rice contributes 6 mg of Vitamin A and 2 mg of Vitamin B. The sodium level in the cereal box must be less than 6 mg and amonut of sodium in oats and rice are 0.4 mg and 0.5 mg respectively. The last constraint is that the box of cereals must contain at least 10 ounces of oats. An ounce of oats cost $0.05 whereas an onuce of rice costs $0.03.

For the optimal solution, what are the slack&surplus variables for Vitamin A, Vitamin B, Sodium and Oats?

Hint: You'll have to calculate the optimal solution first, then move on from there.

Its very easy if you think about it a little. Good luck to all!

Update: Congrats to Batman534.

The solution is:

Vitamin A: 38 surplus
Vitamin B: 0 surplus
Sodium: 1.5 slack
Oats: 0 surplus

As a lot of you asked about slack&surplus, here:

Slack means resources that weren't used for the optimal solutions, surplus means resources exceeded (more than required).

Your objective function is, minimizing cost.

Thus,

Z= cost
x1 =oats
x2=rice

Minimize Z = 0.05 x1 + 0.03x2

If you graph all the constraints and the objective function, you can mark corner points of the feasible region and plug in those cordinates to the objective function. The lowest value will be your optimal solution as you are trying to minimize cost (Z).

To find surplus for Vitamin A, you use the Vitamin A constraint; 8x1 + 6x2 - s1 = 48

8(10) + 6(1) - s1 = 48
s1 = 38

To find surplus for Vitamin B, you use the Vitamin B constraint; x1 + 2x2 - s2 = 12

(10) + 2(1) - s2 = 12
s2 = 0

To find slack for Sodium, you use the Sodium constraint; 0.4x1 + 0.5x2 + s3 = 6

0.4(10) + 0.5(1) + s3 = 6
s3 = 1.5

To find surplus for Oats, you use the Oats constraint; x1 - s4 = 10

(10) - s4 = 10
s4 = 10
 
Originally posted by: Xiety
The sodium level in the cereal box must be less than 6 mg and amonut of sodium in oats and rice are 0.4 mg and 0.5 mg respectively.
!
Click to expand...

i'm assuming this is 0.4mg per ounce?
 
Hehe, I didn't really need the account but I liked playing the game, so I'm giving it away. PM me with your email and answer to riddle:

You have an unlimited water supply, a 5 gallon jug and a 3 gallon jug. How can you fill one of them to exactly 4 gallons.

It's from a movie......
 
Answer was to fill the 5 gallon bucket and use it to fill the 3 gallon bucket. now empty the 3 gallon one and pour the remaining 2 gallons from the 5 gallon bucket to the 3 gallon.
fill the 5 gallon bucket again and use it to fill the three gallon bucket, which leaves you 4 gallons in the 5 gallon bucket.
 
Update: Congrats to Batman534.

The solution is:

Vitamin A: 38 surplus
Vitamin B: 0 surplus
Sodium: 1.5 slack
Oats: 0 surplus

Optimal solution was 10 ounces of oats and 1 ouces of rice. Thanks all for participating!
 
Could have also been: Fill the 3 and dump in the 5, fill the 3 again and dump in the 5 until it is full. This leaves 1 gallon in the 3 gallon jug. Empty out the 5, then dump the 1 gallon that is in the 3 into the 5. Then fill the 3 and dump into the 5. You now have 4 gallons in the 5.
But the other was the one that won it
 
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