Question

Hugo is making a protein shake. He will combine two different shake powders: Powder 1 and Powder 2. One scoop of Powder 1 contains 5 grams of carbohydrates, 22 grams of fat, and 300 calories. One scoop of Powder 2 contains 10 grams of carbohydrates, 14 grams of fat, and 100 calories. If Hugo wants his shake to have at least 1500 calories and at most 50 grams of carbohydrates, how many scoops of each powder should he use to make a shake with as little fat as possible?

Number of scoops of Powder 1:

Number of scoops of Powder 2:

Minimum number of grams of fat:

Answer 1

Let x scoops pf powder 1 and y scoops of powder 2

calories : 300x + 100y >= 1500

carbohydrates : 5x + 10y <= 50

Further : x>=0 ;y >=0

Miniumum use of fat : P(x, y) = 22x + 14y

Now solve graphically :

Check the value of Fat equation P(x,y) = 22x +14y where at which boundary point we get min. value

P(5,0) = 22*5 + 14*0 = 110 gm

P( 4, 3) = 22*4 + 3*14 = 130 gm

P ( 10,0) = 22*10 + 0 = 220 gm

So, minimum fat is 110 gms

No. of scoops of Powder1 =10

No.of scoops ofPowder 2 = 0