1.1. A cargo plane has two compartments in the front and back with weight and volume capacities as listed in the following table. The revenues, volumes, and weights associated with two type of products that could be carried by the cargo plane is given in the following table. Formulate an LP that maximizes the revenue. 1.2. A food manufacturing company provides its products in three types of packaging. The first package includes a garden salad, apple, and a cookie. The second package includes a turkey sandwich, chips, and cookie. The third package includes a roast beef sandwich, chips, and cookie. Production of 1,000 packages of each product requires 0.3,0.2, and 0.2hr of the operation manager respectively. Also, the packaging staff requires 6,3 , and 3 minutes for packing of the three products respectively. The cost of salad, turkey, and roast beef sandwiches are $2,$2, and $3 and they are sold for $8,$7, and $8. During the next month, the company has 400hr production capacity and the manager is available for 40hr. The number of salads produced must be at least 20% of the total production. Formulate an LP that maximizes the profit. 1.3. MCO manufacturing company is planning to produce two types of detergents: D1 and D2. For the production of each unit of D1, 5oz of chemical 1 and 6oz. of chemical 2 are required. Also, the production of each unit of D2 requires 4oz of chemical 1 and 5oz. of chemical 2. Additionally, each day the company has a supply of 1,000oz of chemical 1 and 1,500 oz. of chemical 2. Through a contract, the company is committed to producing at least 100 units of D1 and 120 units of D2. Each unit of chemicals 1 and 2 are purchased for $2 and $3 per oz. I each unit of D1 is sold for $30 and each unit of D2 is sold for $25 formulate a mathematical programming problem which maximizes the company profit