A restaurant, Bob’s Burgers, specializes in making 3 kinds of extra large burger

Question

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.

Explanation / Answer

Hence 37 deluxe, 2 supreme and 10 toppings sold.

Deluxex1 Supremex2 The Giantx3 Total Meat 2 3 5 130 Cheese 1 2 2.5 66 Toppings 1 1.5 3 70 2x1+3x2+5x3 =130 2 3 5 130 x1+2x2+2.5x3 =66 1 2 2.50 66 x1+1.5x2+2.5x3 =70 1 1.5 3 70 R1-2R3 =R1 0 -1 0 -2 R2-R3 =R2 0 0.5 -0.5 -4 1 1.5 2.5 70 x2 = 2 x3= 10 x1+2(2) + 2.5(10) = 66 x1 66-29 37

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