A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer’s profit? (Let P be the profit, W be the number of acres of wheat and B be the number of acres of barley) What is the optimal solution?
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A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer’s profit?
(Let P be the profit, W be the number of acres of wheat and B be the number of acres of barley)
What is the optimal solution?
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- Mack's guitar fabrication shop produces low cost, highly durable guitars for beginners. Typically, out of the 100 guitars that begin production each month, only 82 percent are considered good enough to sell. The other 18 percent are scrapped due to quality problems that are identified after they have completed the production process. Each guitar sells for $260. Because some of the production process is automated, each guitar only requires 88 labor hours. Each employee works an average of 160 hours per month. Labor is paid at $10 per hour, materials cost is $42 per guitar, and overhead is $4,200. a. The labor productivity ratio for Mack's guitar fabrication shop is $26.65 per hour. b. The multifactor productivity ratio for Mack's guitar fabrication shop is (Enter your response rounded to two decimal places.)A group of students organizes a bake sale in which they sell hundreds of cookies at$1 per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables are input variables?a. 1 and 2b. 1 and 3c. 1, 3, and 5d. 1, 3, and 6Kofi Abebrese runs a small industrial company that specialize in the production of high standard windows for housing estates. A worker is paid GHC0.9 per hour and can produce two window with an hour. Each window uses a frame costing GHC1 and incur a variable overheads of GHC0.7. Each window sells for GH¢3. Currently, due to the economic condition, work is rather slack and three employees are occupied in carrying out extensive repairs to Kofi Abebrese's own house. Kofi owns a warehouse next to the factory, which had been used as a factory store, in the past. It is now let out on a renewable annual lease of GHC600. A new building company, Allied Consult, which specializes in the production of prefabricated houses has asked Kofi if he would be interested in accepting a contract for GHC30,000 which will be for a year initially, to produced molded internal building sections. Kofi estimates that, the contract will take 13,200 hours of works, or the work of five men for a year, and that…