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A catering company is planning its menu for an upcoming event. The company wants to offer two types of dishes: Vegetarian and Non-Vegetarian. Due to kitchen capacity and ingredient availability, the company faces the following constraints: The total number of dishes (Vegetarian and Non-Vegetarian) cannot exceed 150. The company needs to serve at least 20 more vegetarian dishes than non-vegetarian dishes to meet the client's request. The profit from serving one vegetarian dish is $8, and the profit from serving one non-vegetarian dish is $12. The company aims to maximize its profit while meeting the above constraints. Formulate the above problem mathematically in the form of a linear programming problem.
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