Matrix, college

Question

2. A concession stand at a city park sells hamburgers, hot dogs, and drinks. Three patrons buy the food and drink combinations denoted in the following table. Patron 1 spends $11, patron 2 pays $5 for the food, and the price of the food for patron 3 is $22. Let x, y and z represent the cost for a hamburger, a hot dog, and a drink, respectively. Set up a system of equations to solve for x, y and z. Then, set up the augmented matrix for the system and solve the system. Explain the solution in the context of the problem. Patron Hamburgers Hot Dogs Drinks 2 3 1 0 3 5 2 a. Identify the variables of the problem using x, y and z. b. Determine the system of equations to be solved. C. Solve the system of equations using Gauss-Jordan Elimination.

Answer 1

The statement of the problem is still incomplete.

You have not given the sales data.

We cannot solve this problem until we have the sales data which

you claim is in a table, 3rd sentence from the bottom.

Please close off this posting and repost with a COMPLETE statement

of the problem.

Answer 2

This seems difficult to answer based on what is shown here. The total cost for a given patron can be represented by an equation such as:

T = Ax + By + Cz

Where T is the total cost, A is the number of Hamburgers purchased, B is the number of Hot Dogs purchased, and C is the number of Drinks purchased. From what you have written, I can’t determine a specific solution, but I can at least help you set up something. The three equations then for the three customers would be:

1) A₁(x) + B₁(y) + C₁(z) = T₁ = $11

2) A₂(x) + B₂(y) + C₂(z) = T₂ = $ 5

3) A₃(x) + B₃(y) + C₃(z) = T₃ = $22

So the augmented matrix would be

_ _

| A₁ B₁ C₁ | $11 |

| A₂ B₂ C₂ | $ 5 |

| A₃ B₃ C₂ | $22 |

_ _