Formulate the Linear Programming algebraic model :

The Sweet Smell Fertilizer Company markets bags of manure labeled “not less than 60 kilos dry weight.” The packaged manure is a combination of compost and sewage wastes. To provide good-quality fertilizer, each bag should contain at least 30 kilograms of compost but no more than 40 kilograms of sewage. Each kilo of compost costs Sweet Smell 5 pesos and each kilo of sewage costs 4 pesos.

The PCC Faculty Cooperative has P250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Cooperatives regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of restrictions of Bureau of Internal Revenue, it is decided that no more than 40% of the investment be placed in bonds.

The advertising agency promoting the new PCC dishwashing detergent wants to get the best exposure possible for the product within the P100,000 advertising budget ceiling placed upon it. To do so, the agency needs to decide how much of the budget to spend on each of its two most effective media: (1) television spots during the afternoon hours and (2) large ads in the Sunday newspaper. Each television spot costs P3,000; each Sunday newspaper ad costs P1,250. The expected exposure, based on industry ratings, is 35,000 viewers for each TV commercial and 20,000 readers for each newspaper advertisement. The agency director, John Ng, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential PCC customers. He decides that at least 5 but no more than 25 television spots should be ordered; and that at least 10 newspaper ads should be contracted.

The famous ABC Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 a.m., 7 a.m., 11 a.m., 3 p.m., 7 p.m., or 11 p.m., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided. ABC’s scheduling problem is to determine how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day’s operation.