Linear Algebra A restaurant Bobs Burgers specializes in maki

Linear Algebra:

A restaurant, Bob’s Burgers, specializes in making 3 kinds of extra large burgers: The Deluxe, The Supreme, and The Giant. For each Deluxe burger sold, the restaurant uses $2 worth of patty meat, $1 worth of cheese, and $1 worth of toppings. For each Supreme burger sold, the restaurant uses $3 worth of patty meat, $2 worth of cheese, and $1.50 worth of toppings. For each Giant burger sold, the restaurant uses $5 worth of patty meat, $2.50 worth of cheese, and $3 worth of toppings. Let x₁ equal the number of Deluxe burgers sold, x₂ equal the number of Supreme burgers sold, and x₃ equal the number of Giant burgers sold. On an average day, the restaurant spends $130 worth of patty meat, $66 worth of cheese, and $70 worth of toppings. Write a vector equation whose solution gives the number of each burger sold in order for the restaurant to spend these amounts, then state the number of each burger sold on an average day.

Solution

given x1 equal the number of Deluxe burgers sold, x2 equal the number of Supreme burgers sold, and x3 equal the number of Giant burgers sold

Deluxe burger sold, the restaurant uses $2 worth of patty meat

For each Supreme burger sold, the restaurant uses $3 worth of patty meat

For each Giant burger sold, the restaurant uses $5 worth of patty me

so 2x1 + 3x2 +5x2 = $130

Deluxe burger sold, the restaurant uses$1 worth of cheese

Supreme burger sold, the restaurant uses$2 worth of cheese,

Giant burger sold, the restaurant uses $2.50 worth of cheese

so 1x1 + 2x2 + 2.5x3 = $66

x1 +2x2 +2.5x3 = $66

similerly

1x1 + 1.5x2 + 3x3 =$70

x1+1.5x2 +3x3 = $70

now we have to slove these three equations

2x1 + 3x2 +5x2 = $130

x1 +2x2 +2.5x3 = $66

x1+1.5x2 +3x3 = $70

after solving we get x1 =37, x2 = 2 , x3=10

so the number of each burger sold on an average day Deluxe is 37, The Supreme is 2, and The Giant is 10