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- 3. A shop owner blends a fancy brand of tea with a cheaper brand. The fancy brand sells for $5 per pound, and the cheaper brand sells for $2 per pound. How much of each should the owner mix to have 30 pounds worth $3.69 per pound? (Be sure to define your variables and show all your work for full credit.)Enormous State University's Business School is buying computers. The school has two models from which to choose, the Pomegranate and the iZac. Each Pomegranate comes with 400 GB of memory and 80 TB of disk space; each iZac has 300 GB of memory and 100 TB of disk space. For reasons related to its accreditation the school would like to be able to say that it has a total of at least 41,000 GB of memory and at least 11,000 TB of disk space. If the Pomegranate and the iZac cost $3,000 each, how many of each should the school buy to keep the cost as low as possible? HINT [See Example 4.] (If an answer does not exist, enter DNE.) Pomegranate computers___________ iZac computers_________The owner of an apartment building can rent all 50 apartments if she charges $1,700 per month, but she rents one fewer apartment for each $50 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $1,700, $1,750, and $1,800. No. of Apts 50 49 48 Rent Total Revenue $1,700 $ $1,750 $ $1,800 $ (b) Does her revenue from apartment rentals increase or decrease as she increases the rent from $1,700 to $1,800? O revenue increases O revenue decreases = (c) Write an equation that gives the revenue R, from apartment rentals if she makes x increases of $50 in the rent. R(x) (d) Find the rent she should charge to maximize her revenue. $ per month
- Dr. Gurzick owns a computer store and is looking to determine an optimal amount of inventory. He sells laptops, pcs, and tablets. each laptop uses 1 processor, 1 hard drive, 3 sticks of ram, and 1 power supply. they sell for 300. each pc uses 2 processor, 2 hard drive, 3 sticks of ram, and 1 power supply. they sell for 500. each tablet uses 1 processor, 0 hard drives, 2 sticks of ram, and 1 power supply. they sell for 200. on hand I have 500 processors, 300 hard drives, 1000 sticks of ram, and 500 power supplies. Develop a linear programming model for this problem indicating what inventory should be selected to maximize profit by using excel.Let's say there are two sectors of an economy, firms and households. Each household supplies labor to the firms. Households earn $100 per month, they spend $1 per mile to commute to work and they spend $50 on all other goods. Firms produce 1 ton of goods and earn $100 per month net profits on production, but must pay $10 per ton mile to ship its output to the port. All firms, residents use 1 acre of land. Calculate each sector's bid rent function. That is, what is each sector's ability to pay for a location as a function of distance to the center? How far from the center will land use change from business use to residential? Draw a graph of the sector's bid rent function as a function of distance from the center. Be sure to label the graph and describe the location of each sector.Enormous State University's Business School is buying computers. The school has two models from which to choose, the Pomegranate and the iZac. Each Pomegranate comes with 400 GB of memory and 80 TB of disk space; each iZac has 300 GB of memory and 100 TB of disk space. For reasons related to its accreditation the school would like to be able to say that it has a total of at least 62,000 GB of memory and at least 16,400 TB of disk space. If the Pomegranate and the iZac cost $2,000 each, how many of each should the school buy to keep the cost as low as possible? HINT [See Example 4.] (If an answer does not exist, enter DNE.) Pomegranate computers computers iZac
- 1. The church youth group is selling snacks to raise money to attend their convention. Amy sold 2 pounds of candy, 3 boxes of cookies and 1 can of popcorn for a total sale of $65. Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sale of $140. Paula sold 8 pounds of candy, 8 boxes of cookies and 5 cans of popcorn for a total sale of $250. What is the cost of each item? ($20 candy, $5 cookies, $10 popcorn) [USE CRAMER'S RULE] I 2. After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 4 t-shirts, the video, and 1 stuffed animal, their total is $135. Another family buys 2 t-shirts, the video, and 3 stuffed animals for their nieces and spends $115. A third family buys 2 t-shirts, the video, and 1 stuffed animal and their total is $85. What is the cost of each item? [USE G-J ELIMINATION]Two employees (Molly and Jim) must conduct a data analysis project on the success of a firm’s marketing efforts and then write a report of their findings for consideration by the firm’s board. If the first employee, Molly, worked completely alone, she could finish the data analysis component of the project with 30 hours of work and could write the report with an additional 10 hours of work. If Jim worked alone, he would take 48 hours of work to conduct the data analysis and then 12 hours to write the report. Assume that both employees need to contribute to the project, that there would be no benefits to having two people work on the same part of the project (data analysis and writing), and that working on the two parts are independent (i.e. there is no benefit to working on both parts). Which employee has the comparative advantage in conducting the data analysis? ExplainThe Vintage Restaurant, on Captiva Island near Fort Myers, Florida, is owned and operated by Karen Payne. The restaurant just completed its third year of operation. Since opening her restaurant, Karen has sought to establish a reputation for the Vintage as a high-quality dining establishment that specializes in fresh seafood. Through the efforts of Karen and her staff, her restaurant has become one of the best and fastest growing restaurants on the island. To better plan for future growth of the restaurant, Karen needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. Table 17.25 shows the value of food and beverage sales ($1000s) for the first three years of operation. Dependent variable: What is the variable: ___________________________________________ How it is measured, i.e. what units or categories are used (e.g., revenue measured in “dollars”; height measured as “short, average, tall”)…
- A carpenter builds bookshelves and tables for a living. Each bookshelf takes one box of screws, two 2 ✕ 4's, and three sheets of plywood to make. Each table takes two boxes of screws, two 2 ✕ 4's, and four sheets of plywood. The carpenter has 55 boxes of screws, 70 2 ✕ 4's, and 115 sheets of plywood on hand. In order to maximize their profit using these materials on hand, the carpenter has determined that they must build 10 shelves and 20 tables. How many of each of the materials (boxes of screws, 2 ✕ 4's, and sheets of plywood) are leftover, when the carpenter builds 10 shelves and 20 tables? The carpenter has _ boxes of screws, _ 2 ✕ 4's, and _ sheets of plywood leftover.3. A political toy company manufactures stuffed donkeys and elephants using cotton and polyester. At present, 40 units of cotton and 30 units of polyester are available. A donkey sells for $4 and requires 1 unit of cotton and 1 unit of polyester. An elephant sells for $5 and requires 2 units of cotton and 1 unit of polyester. Formulate an LP that will help the company maximize profit.A financial manager has to invest $ 200000 in two options, one risky with a return of 20% and second less risky with a return of 10% per year. If the goal is to make $ 32000 at the end of the year what should be distribution of the money in both options.