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?

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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