Anton is making a protein shake. He will combine two different shake powders: Po

Question

Anton is making a protein shake. He will combine two different shake powders: Powder 1 and Powder 2. One scoop of Powder 1 contains 3 grams of carbohydrates, 12 grams of protein, and 240 calories. One scoop of Powder 2 contains 6 grams of carbohydrates, 2 grams of protein, and 80 calories. If Anton wants his shake to have at most 3600 calories and at most 90 grams of carbohydrates, how many scoops of each powder should he use to make a shake with as much protein as possible? Number of scoops of Powder 1: Number of scoops of Powder 2: Maximum number of grams of protein:

Explanation / Answer

Number of scoops of Powder 1 = x

Number of scoops of Powder 2 = y

Maximixe , Z = 12x + 2 y

Subject to

3x + 6y <= 90

240x + 80y <= 3600

Where, x>=0, y> =0

Solving this using online calculators we get

x =15, y =0

So, number of scoops of Powder 1 = 15

Number of scoops of Powder 2 = 0

Maximixe , Z = 12*15 + 2*0 = 180 grams

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.