-2 20 1,0 1,0 The above is the graph of a system of linear inequality constraints. The corner points of the graph are: (5, 18), (13, 20), (15, 12), (9, 2) Find the maximum value of x = -5x + 2y over the graph. The maximum value of z is at the corner point
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- A college student works in both the school cafeteria and library. She works no more than 12 hours per week at the cafeteria, and no more than 16 hours per week at the library. She must work at least 20 hours each week. Write a system of inequalities that describes all the given conditions. Write a system of inequalities letting x= number of hours worked at the cafeteria per week and y = number of hours worked at the library per week. x+yz x≤ ysFind the point of intersection of the pair of straight lines. y = −7x − 10 −y = 8x + 2 (x, y) =Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.
- Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 2), (0, 3), (2, 2), (2, 0), (1, 1), (2, 1), (3, 3)}. (a) Draw the directed graph of R. (b) Is R reflexive? Explain. (c) Is R symmetric? Explain. (d) Is R transitive? ExplainFind the exact solution of the homogeneous equation xy 2 dy 3 3 (d) x = y³ - x³, y(1) = 2Suppose Box I contains five red balls and two white ones while Box II contains one red and four white ones. A box is chosen at random by selecting a random number from 0 through 9. If a 1 or 2 is selected, Box I is chosen; otherwise Box II is chosen. If I took Box 1 and chose 2 balls without replacement, what is the proabability that exactly one would be red?
- For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculatoWe are going to see the movie Fatal Repulsion. Thereare three parking lots we may park in. One is one block eastof the theater (call this lot 1); one lot is directly behindthe theater (lot 0); and one lot is one block west of thetheater (lot 1). We are approaching the theater from the east.There is an 80% chance that lot 1 will have a vacantspace, a 60% chance that lot 0 will, and an 80% chance thatlot 1 will. Once we pass a lot, we can’t go back to it. Assumethat when we are at a given parking lot, we can determinewhether it has any vacant spaces, but we can’t see any ofthe other lots. Our dates for the evening will assess us apenalty equal to the distance (in blocks) that we park fromthe theater. If we find no space, they will assess a penaltyof 10 (and never go out with us again). What strategyminimizes our expected penalty? Answer the same questionif there is a 70% chance that lot 0 has a vacant space.
- Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O OThere are 2657 professors in a college out of which one ofthem has to be selected for promotion through a game.Everyone will sit in a circle with numbered chairs. Each ofthem will evict the professor to his left, starting from the firstchair, and this cycle will go on until one last professor is left.Now you are one of the professors, which chair would youpick to ensure you get promoted?Player A and B play a game in which each has three coins, a 5p, 10p and a 20p. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, then A wins B’s coin. But, if the sum is even, then B wins A’s coin. Find the best strategy for each player and the values of the game.