Linear Programming

The linear programming categorized as maximum and minimum by solving graphical method, simplex method, transportation method.

7-42. The Marriott Tub Company manufactures two lines of bathtubs, called model A and model B. Every tub requires a certain amount of steel and zinc; the company has available a total of 25,000 pounds of steel and 6,000 pounds of zinc. Each model A bathtub requires a total of 125 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. Each model B bathtub can be sold for a profit of $70; it in turn requires 100 pounds of steel and 30 pounds of zinc. Find the best production mix of the bathtubs.

7-43. The Sweet Smell Fertilizer Company markets bags of manure labeled "not less than 60 pounds 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 pounds of compost but no more than 40 pounds of sewage. Each pound of compost costs Sweet Smell 5 cents and each pound of sewage costs 4 cents. Use a graphical LP method to determine the least cost blend of compost and sewage in each bag.

7-44. The National Credit Union has $250,000 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%. Credit union regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as Cleveland and New York, it is decided that no more than 40% of the investment be placed in bonds. How much should the National Credit Union invest in each security so as to maximize its return on investment?

7-45. The advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $100,000 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 city's Sunday newspaper. Each television spot costs $3,000; each Sunday newspaper ad costs $1,250. 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, Mavis Early, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential Breem customers. She 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. How many times should each of the two media be used to obtain maximum exposure while staying within the budget? Use the graphical method to solve.

7-46. Androgynous Bicycle Company (ABC) has the hottest new products