Explain A linear programming computer package is needed. Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf speakers and 4,100 floor speakers over the next two months, with the following delivery schedule. Model Month 1 Month 2 2,100 1,200 Bookshelf Floor 1,500 2,600 Greenville estimates that the production time for each bookshelf model is 0.7 hours and the production time for each floor model is 1 hour. The raw material costs are $10 for each bookshelf model and $12 for each floor model. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2400 hours of regular production time available each month and up to 1000 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. Round your answers to the nearest integer. (Let BaR = regular bookshelf units for month 1, BbR = regular bookshelf units for month 2, FaR = regular floor units for month 1, FDR = regular floor units for month 2, Bao = overtime bookshelf units for month 1, Bbo = overtime bookshelf units for month 2, FaO = overtime floor units for month 1, and Fbo = overtime floor units for month 2) (BaR, BbR, Far, FØR, Bao, Bbo, Fao, FDO) – ( 1228.57,871. 42,0.1200,0,15400,2400,160,40 X Total Production Cost = $ 241130

Recent research by economists David Cutler, Edward Glaeser, and Jesse Shapiro on Americans’ increasing obesity points to improved technology in the preparation of tasty and more caloric foods as a possible explanation of weight gain. Before World War II, people rarely prepared French fries at home because of the significant amount of peeling, cutting, and cooking required. Today, French fries are prepared in factories using low-cost labor, shipped frozen, and then simply reheated in homes. Paul consumes two goods: potatoes and leisure, N. The number of potatoes Paul consumes does not vary, but their tastiness, T, does. For each extra unit of tastiness, he must spend p_t hours in the kitchen. Thus, Paul’s time constraint is N + p_tT = 24. Paul’s utility function is U = TN^0.5.

a. What is Paul’s marginal rate of substitution, MU_T /MU_N?

b. What is the marginal rate of transformation, p_T / p_N?

c. What is Paul’s optimal choice, (T*, N*)

d. With a decrease in the price of taste (the ability to produce a given level of tastiness faster), does Paul consume more taste (and hence gain weight) or spend more of his time in leisure? Does a decrease in the price of taste contribute to weight gain?