Solve for the following Linear Programming Models

1. A certain company wants to advertise its new product and wishes to allocate P 2,000,00 towards advertising in newspapers and magazines . The intension of the company is to maximize the exposure of its advertisements. Each half- page of the leading newspapers costs P 200,000 and each page of a magazine costs P 300,000. It is guaranteed that each page of the magazine will reach the audience of 250,000 ,while 450,00 persons will read each half page of the newspaper advertisement. Furthermore, it is specified that at least one page of the magazine and half-page newspaper will be allocated for the companys advertisement. Find the number of advertisement on magazines and newspapers advertisements that will maximize exposure and still remain within the P 2,000,000 budget.

2. The travel agency has sold 1,800 tickets for International IT Annual Convention in Singapore. The weekend package includes airfare and there is a choice of two types of airplanes for the charter flights. Type A can carry 100 passengers and type B can carry 300 passengers.. Each flight of type A aircraft will cost P 9,000 and each type B flight will cost P 15,000. The agency is allowed to lease no more than 12 planes. Each type A flight requires 2 stewards and each type B flight requires 3 stewards. No more than 30 stewards are available. How many airplanes of each type should be leased in order to minimize the cost?