For the remaining questions, consider the following problem description:An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costsC1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possiblesites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the correspondingsite. ntsnsProvide the best interpretation of the constraint:OX3 + X5 ≤ 1X₁ + X5 ≤ 1Exploring site S3 or site S4 prevents you from exploring site S5OExploring site S3 requires exploration of S4 or S5Exploring sites S3, S4, and S5 is only possible if another constraint is disjunctiveExploring the combination of sites S3 and S4 prevents you from exploring S▸4

In the context of optimization problems, a constraint is a condition or limitation that restricts…

Answered: For the remaining questions, consider…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Social Night Problem 2: In the above diagram, on the left, we have some girls and on the right, we have some guys. If there is an edge between a girl and a guy, it means both of them are attracted to each other. Yes, a person can have multiple crushes. In this scenario, what is the maximum number of couples that can result from the above diagram given that nobody wants to end up with someone they don't like? A person would rather stay single than end up with someone they don't like. What matching algorithm are you using for this problem? Show each step of your algorithm precisely.
6. (a) A man has $4.55 in change composed entirely of dimes and quarters. What are the maximum and minimum number of coins that he can have? Is it possible for the number of dimes to equal the number of quarters? (b) The neighborhood theater charges $1.80 for adult admissions and $.75 for children. On a particular evening the total receipts were $90. Assuming that more adults than children were present, how many people attended? (c) A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum is 114. How many of each were there originally?
a.) Make a list of the amounts of money one can have that cannot be reduced to a smaller number of coins. (Hint: there are seven possible amounts.) One of the amounts is (d+e). b.) Make an addition table for Glosian money. It should be a seven by seven table, with a row and column for each of the amounts you found in the previous problem. For example, your table shouldshow that (d+e)+d=f c.) One of the seven amounts you found in the previous problem can be considered to be the zero of Glosian money, since adding it to a collection of coins does not change the collection’s value (after trading to get the smallest possible number of coins, of course.) Which amount is the zero forGlosian money? d.) The opposite of an amount is the amount you add to it to get the zero. Find the opposite of each of the seven amounts.
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next…
3 The ordering and trans Portation cost C (in hundreds of dollars) for an automobi le dealership is modeled by C=6 + where X is the number of automobiles ordered. tind the Open interuals on which the cost is increasing or decreasing.
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,500, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,900. Manufacturing costs are $13 for each 4-cylinder connecting rod and $16 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week s4 = 1 if the production line is set up to…
Another issue to research when purchasing ahome is that of points and mortgage interestrates. Usually paying higher points results in alower mortgage interest rate. The question forthe homebuyer is: Should I pay higher points fora lower mortgage interest rate, or pay lowerpoints for a higher mortgage interest rate? Theanswer to that question depends on manyfactors, one of which is the amount of time thehomeowner plans on staying in the home.Consider two typical situations for a 30-year,$100,000 mortgage. Option 1 offers an annualmortgage interest rate of 8.25% and a loanorigination fee of 3.5 points. Option 2 offers anannual interest rate of 8% and a loan originationfee of 4points. What is the total amount paid, including points, after 3 years for each option? ( Round your answers to the nearesr cent.) Option 1:Option 2:
7. Which of the following ordered pairs is within the solution set to the following system of Inequalitles? 22 +y- 11 (y+1)? O (-1, -3) O No solution O (1, 4) O (6, -2) ctla esc #3 & * 4. 6 7 8. W e
Refer to the production possibilities curves for Chairland and Tableland. Chairland can produce 36 chairs per day and no tables, or 18 tables table per day and no chairs. Tableland can produce 40 chairs per day and no tables, or 40 tables per day and no chairs. If the two countries split the difference between the buyer's willingness to pay for tables and the seller's willingness to accept, in terms of the number of chairs for 1 table, the terms of trade will be . (Enter your response rounded to one decimal place.) Country Quantity per day Opportunity cost of chairs Opportuity cost of tables Tableland 40 chairs, 40 tables 1 table 1 chair Chairland 36 chairs, 18 tables 1/2 table 2 chairs
32. A hardware company sells a lot of low-cost, highvolume products. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (30,000), the company can sell theproduct for $20 per unit. If sales are high (70,000),a competitor will enter and the company will be ableto sell the product for only $15 per unit. The variablecost per unit has a 20% chance of being $10, a 60%chance of being $11, and a 20% chance of being $12.Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is…

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