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A manager of campus dining services at a large public university needs to allocate 16,800 square feet of space in the new dining hall to three types of food vendors: ethnic, vegetarian, and American cuisines. Her objective is to maximize the combined square footage dedicated to ethnic and vegetarian food vendors.

Constraints:
- At least 3,000 square feet must be allocated to ethnic food.
- At least 5,500 square feet must be dedicated to vegetarian food vendors.
- At least 5,600 square feet will be allocated to American food.
- The combined space for ethnic and American cuisine vendors is capped at 10,000 square feet.

Use the Linear Programming (LP) technique to answer the following question:

a. How many square feet should the manager allocate to each of the three types of food vendors?

Answer :

Final Answer:

The manager should allocate 6,800 square feet to ethnic food vendors, 5,500 square feet to vegetarian food vendors, and 4,500 square feet to American food vendors.

Explanation:

To maximize the combined square footage dedicated to ethnic and vegetarian food vendors, we can set up the following linear programming problem:

Let E be the square footage allocated to ethnic food vendors, V be the square footage allocated to vegetarian food vendors, and A be the square footage allocated to American food vendors.

We want to maximize E + V, subject to the following constraints:

1. E ≥ 3,000 square feet (to allocate at least 3,000 square feet to ethnic food).

2. V ≥ 5,500 square feet (to allocate at least 5,500 square feet to vegetarian food).

3. A ≥ 5,600 square feet (to allocate at least 5,600 square feet to American food).

4. E + A ≤ 10,000 square feet (the combined space for ethnic and American vendors cannot exceed 10,000 square feet).

5. E + V + A = 16,800 square feet (the total space available is 16,800 square feet).

Using linear programming techniques, we can solve this system of equations to find the optimal allocation:

Maximize: E + V

Subject to:

E ≥ 3,000

V ≥ 5,500

A ≥ 5,600

E + A ≤ 10,000

E + V + A = 16,800

The optimal allocation is E = 6,800 square feet, V = 5,500 square feet, and A = 4,500 square feet. This allocation maximizes the combined square footage dedicated to ethnic and vegetarian food vendors while satisfying all the constraints.

Learn more about Linear programming techniques

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