After taking a nutrition class a big macaroni and cheese fan

After taking a nutrition class, a big macaroni and cheese fan decides to improve the levels of protein and fiber in her favorite lunch by adding broccoli and canned chicken. The nutritional information for the foods referred to in this exercise is given in the table below. Complete parts (a) and (b) below. If she wants to limit her lunch to 390 calories but get 30 grams of protein and 10 grams of fiber, what proportions of servings of macaroni and cheese, broccoli, and chicken should she use? She should use servings of macaroni and cheese, servings of broccoli, and Q servings of chicken to get her desired nutritional content. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Solution

we will do it by using matrix the following equations we will have

269x+52y+69z=390

9x+5.4y+16z=30

x+5.2y+0z=10

so we will solve for like this way

Your matrix

Find the pivot in the 1st column and swap the 3rd and the 1st rows

Multiply the 1st row by 9

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by 269

Subtract the 1st row from the 3rd row and restore it

Make the pivot in the 2nd column by dividing the 2nd row by -41.400000000000006

Multiply the 2nd row by 5.2

Subtract the 2nd row from the 1st row and restore it

Multiply the 2nd row by -1346.8

Subtract the 2nd row from the 3rd row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by -451.5024154589371

Multiply the 3rd row by 2.009661835748792

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by -0.38647342995169076

Subtract the 3rd row from the 2nd row and restore it

Solution set:

x1 = 0.914285102877135=0.91

x2 = 1.7472528648313201=1.75

x3 = 0.7710167877510418=0.77

	X1	X2	X3	b
1	269	52	69	390
2	9	5.4	16	30
3	1	5.2	0	10