Given binary relation, R ={(4,4), (4,5), (4,6), (4,7), (5,5), (5,6), (5,7), (6,6), (6,7), (7,7) } is defined on set AF{ 4,5,6,7 Is the relation is reflexive? O True O False
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- A person sells and installs A, B and C. The table shows, for example, that it takes 3 hours to sell a unit of B, it takes 4 hours to install it, and net profit per unit is $ 40. Product No. of Units Selling Hours per Unit Installation Hours per Unit Profit per Unit A x 1 1 $10 B y 3 4 40 C z 2 1 10 During a 38-hour week, the person allots no more than 18 hours to selling and no more than 20 hours to installation. Find the combination of number of units of A, B, C that would yield maximum profit.A company has one machine which can be used to make product Alpha and product Beta. Each unit of product Alpha requires 45 minutes of machine time, while each unit of product Beta requires 37 minutes of machine time. The machine can be used for 8 hours per day and 5 days per week. Next week the company will produce 23 units of product Alpha. After completing the production of Alpha, the company will produce product Beta. How many units of product Beta can be produced next week? Use at least 4 decimals.You must showm your calculation steps and brief explanation on your Excel spreadsheets.Consider an ARIMA(2,1,1) process. Write out the resulting model usinga. Backshift notation with the backshift operator B.b. Backshift notation with the operatorc. No backshift notation
- A manufacturer produces both widgets and gadgets. Widgets generate a profit of $70 each and gadgets have a profit margin of $45 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $500 for gadgets. Widgets consume 5 units of raw material A and 6 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 500 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets.Set up the problem in Excel and find the optimal solution. (Leave no cells blank — be certain to enter "0" wherever required. Round your answers to 2 decimal places.) (Round your answer to 2 decimal places.)A manufacturer produces both widgets and gadgets. Widgets generate a profit of $25 each and gadgets have a profit margin of $75 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $300 for gadgets. Widgets consume 6 units of raw material A and 8 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 400 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution. The manufacturer will produce .......widgets and ...... gadgets the manufacturer's profit will be ......TRUE OR FALSE The simplex method is a linear programming procedure designed to handle only three variables
- Home mortgage lenders often charge points on a loan in order to avoid exceeding a legal limit on interest rates or to make their rates appear competitive with those of other lenders. As an example, with a two-point loan, the lender would loan only $98 for each $100 borrowed. The borrower would receive only $98 but would have to make payments just as if he or she had received $100. In this way, the lender can make more money while keeping his or her interest rate lower. Suppose that you receive a loan of $260,000 payable at the end each month for 30 years with an interest rate of 9% compounded monthly, but you have been charged three points. What is the effective interest rate on this home mortgage loan?A manufacturer produces both widgets and gadgets. Widgets generate a profit of $50 each and gadgets have a profit margin of $40 each. To produce each item, a setup cost is incurred. This setup cost is $300 for widgets and $400 for gadgets. Widgets consume 5 units of raw material A and 4 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 600 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution.Suppose that a firm makes gears (G) and axles (A). Each gear requires 0.75 hours of labor and each axle requires 1.25 hours of labor. Six thousand minutes of labor are available. How should the labor constraint(s) be written? 0.75G + 1.25A ≤ 6000 0.75G + 1.25A ≤ 100 0.75G + 1.25A ≥ 6000 45G + 75A ≤ 100 45G + 75A ≤ 1000
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