Answer the following questions on linear programming (use the class notes to review the concepts).1. a manager has formulated the following lp problem. draw the graph and find the optimal solution. (in each, all variables are )maximize: 10x+15y, subject to 2x+5y ≤ 40 and 6x+3y ≤ 48.2. an athlete carefully watches her intake of calcium, protein, and calories. her breakfast diet consists mainly of milk and cereal, whose prices andnutrient contents appear in the following table: milk (1 oz.) cereal (1 oz.)calcium22protein26calories62pri ce$.10$.15she seeks a diet that supplies at least 50 units of calcium, 90 units ofprotein, and 66 calories at minimum cost. a. formulate, graph, and solve this decision problem. what is theminimum cost of meeting the nutrient requirements? (9)b. if the calcium requirement is increased by a small amount, say 4 units to 54, then find the new solution and the shadowprice associated with calcium.(3)

How can a poor housing market put home buyers in a financially unstable position? a. changing property values means it’s easier to find homes with low rental costs. b. when the home value decreases, property taxes and insurance costs increase. c. houses are valued lower than their purchase prices, so the home equity decreases. d. home buyers lose all tax benefits and tax incentives when the housing market goes down. e. mortgage payments can increase even though the home value decreases.

The hawthorne works was a large western electric factory with 45,000 employees. during the 1920s and 1930s, hawthorne works was the site of some well-known industrial studies. in one of the studies, researchers investigated the impact of different working conditions on worker productivity. prior to the start of the study, researchers secretly measured workers' productivity for several weeks. then researchers chose two workers, who then chose their own teams. the teams were separated from the general workforce and completed their work in different experiment rooms where the researchers could observe them more easily. over a 5-year period researchers manipulated the structure of the workday for each team (number and duration of breaks and number of hours per shift). for each of these changes in working conditions, the researchers measured the effect on productivity. for some conditions, such as frequent short breaks, workers rebelled by intentionally decreasing productivity. why did the researchers secretly measure the workers' productivity before creating the two treatment groups? a, to create similar treatment groups so that a cause-and-effect relationship could be establishedb, to draw conclusions about the productivity of all workers in the plant based on the test groupsc, to directly control for confounding variablesd, to provide a baseline for measuring worker productivity

What is the best definition of a conclusion?