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 4 grams of carbohydrates, 28 grams of fat, and 270 calories. One scoop of Powder 2 contains 8 grams of carbohydrates, 4 grams of fat, and 90 calories. If Hugo wants his shake to have at least 2700 calories and at most 80 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

Here scoops of powder 1 is x unit and scoops of powder is y unit.

so minimize the fat

Minimize

Z = 28x + 4y

Constraints are

4x + 8y 80

270x + 90y 2700

so here by solving by graphical method. we get critica points are (10,0), (20,0) and (8, 6)

so Here for each critical we will calculate the total amount of fat

for (10,0)

Total fat = 28 * 10 = 280

for (20, 0)

Total fat = 28 * 20 = 560

for (8, 6)

Total fat = 28 * 8 + 6 * 6 = 260

so here the optimum point is (8 gm, 6 gm)

Number of scoops of Powder 1: 8 gm

Number of scoops of Powder 2: 6 gm

Minimum number of grams of fat: 260 gm