please help me answer the following in a step by step process

1. Which of the following is the correct illustration of the feasible region for the given LP model below? Minimize = = 4x + By subject to: + + 1.by > 45 2r + 0.5y 2 40 J.y20 B. H A. Option 1 Option 2 C. D. + Option 3 Option 42t}. NUT INCLUDED a. t}. c. d 21. The feasible region: a. may range over al positive or negative values of only one decision vanatile b. is an area hounded by the oolleclive constraints and represents all pemv'ssihle combinations of the decision variaoies c. represents all values of each constraint d. is dened by the objective function 22. The northwest corner rule requires that we start allocating units to shipping routes in the: a. louver right comer of the table b. upper right comer of the table c. highest oostly cell of the table d. Upper left-hand corner of the tatile 23. The purpose of a dummyr source or dummy destinaon in a transportation problem is to a. obtain a balance behireen total supply and total demand to. make certain that the total cost does not exceed some specied gure c. m the solution from becoming degenerate d. m a means of representing a dummy problem 24. 1Itil'hat is the cost of the transportation solution shown in the table? a. $1351] t}. 51151] c. $10M d. $1231] 25. Operations research is the application of methods to arrive at the optimal solutions to the problems. a. Economical E}. Scientic c. Both a and b d. Futisc 26. Operations management can be dened as the application of to a problem within a system to yield the optimal solution. a. suitable manpower b. mathematical techniques, models, and tools c. nancial operations d. resources 2?. The objective function and constraints are functions of two types of gg'ggggl variables and van'ables. a. positive and negative b. controllable and uncontrollable c. strong and weal: d. none of the above 23. Operations research techniques help the directing authority in optimum allocation of various limited resources like a. men and machine b. money c. material and time d. all of the above 29. 1il'il'hat is the objective function in linear programming problems? a. A constraint for available resource b. An objective for research and development of a company c. A linear function in an optimization problem d. A set of nonnegativity conditions 311}. 1llli'hich statement characterizes standard form of a linear programming problem? a. Constraints are given by inequalities of any type b. Constraints are given by a set of linear equations b. Cor'straints are given onlyr by inequalities of greater than or emal to type d. Constraints are given only by inequalities of less than or equal to type 31. In graphical method, the restn'ction on number of constraints is a. 2 b. not more than 3 c. 3 d. none of the above 33. Identify the type of the feasible region given by the set of inequalities below, Iivhere both 3: and v are positive. 1: ._ 3.! s 1 x 1v 5 2 a. A tn'angle b. A rectangle c. An unbounded region d. An empty:r region 33. The feasible region of a linear programming probiem has four extreme points: goo}, Bit ,1}, C{D,1}, and l]1[1,}. Identity an optimal solution for minimization problem with the objective function I = 2 I 2 v. a. A unique solution at C b. A unique solutions at D c. An atternative solution at a line segment between A. and B d. An unbounded solution 34. 1I.I'I.I'hich technique is used in nding a solution for optimizing a given objective, such as prot maximization or cost reduction under certain constraints? a. Linear Programming models b. ueu'ng Models c. Inventoryr Models kl. Project Scheduling 35. If you flipped a coin, what is the probability it will land on heads? 1 36. A card is selected from a deck of playing cards. What is the probability of selecting a red card? 1 37. You pick a marble from this bag. What is the probability you will choose either a black or white marble? IL 3/5 4/10 1/10 3/1038. How many outcomes are there with tossing a coin and rolling a dice? N 12 24 39. The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than "A"? 2/7 5/7 5/49 10/49 40. The tree diagram shows the outcomes of rolling a die and flipping a coin. What is the probability of rolling an even number and flipping a head? Die Coin H TH 1/4 1/2 1/3 3/441. The following M & M's colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a brown candy? 1/9 1/10 3/20 1/4 42. How many total outfit options are represented? Sneakers Jeans Sandals T-Shirt Sneakers Khakis Sandals Sneakers Jeans Sandals Outfits Polo Shirt Sneakers Khakis Sandals Sneakers Jeans Sandals Sweater Sneakers Khakis Sandals43. How many outcomes when choosing a vowel (a, e, i o, u) and then a number (2 or 6)? 5 6 10 12 44. Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. [Let "L" designate "locked" and U" designate "unlocked" ] List the outcomes of the sample space. (LLU, LUL, ULL, UUL, ULL, LUU} (LLL, UUU} (LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} None of these45. A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Less than 3). 1/4 2/3 1/12 1/6 46. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? 564 645 735 756 47. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? 5 10 15 202. How many corner points are there in this LP problem? Minimize = =4r + 8y subject to: r + 1.5y > 45 2r + 0.5y 2 40 r+ 40 I.V 20 a. 1 b. 2 C. 3 d. 4 3. Which of the following points is a corner point in the feasible region which provides the optimal solution for this LP problem? 1 point Minimize : = 4r + 8y subject to: r + 1.5y > 45 2r + 0.5y 2 40 styx 40 a. (0, 30) b. (30,10) C. (15, 20) d. (40,0)48. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? 266 5040 11760 86400 49. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? 32 48 36 60 50. How many 4 - letter words with or without meaning, can be formed out of the letters of the word, "LOGARITHMS', if repetition of letters is not allowed? 40 400 5040 25204. Which of the following is the optimal value of the objective function for the LP model in this problem? Minimize = = 4r + By subject to: r + 1.5y 2 45 2r + 0.59 2 40 cty5 40 r.1/20 a. 240 b. 220 c. 200 d. 160 5. A linear programming problem has objective function P = 3x+2y and the following linear inequality constraints below. How many slack variables are needed for the simplex algorithm? x-y50, xtys3, x20, y20 a. 1 b. 2 C. 3 d. 46. The objective function for a linear programming problem is P = 3x +2y- z. What is the correct way to arrange this equation in order to enter it into a Simplex Tableau? a. P = 3x + 2y - z b. -3x - 2y + P = z Option 1 Option 2 C. -3x - 2y + z + P = 0 d. 3x + 2y - z - P = 0 Option 3 Option 4 7. Let x = number of units of product 1 to produce and let y = number of units of product 2 to produce. Consider the following objective function below. What will the optimal objective function value be? Maximize z = x + 2y Subject to: x + y s 12 [resource A). x $ 8 (resource B), y s 6 (resource C), xy 20 a. 10 b. 12 C. 16 d. 188. Suppose the amount resource A available is increased from 12 to 14. Now what will the optimal objective function value be? Maximize z = x + 2y Subject to: x + y = 12 (resource A). x $ 8 (resource B], y s 6 (resource C). xy 20 a. 16 b. 18 c. 20 d. 249. Suppose the amount resource B available is increased from 8 to 10. Now what will the optimal objective function value be? Maximize z = x + 2y Subject to: x + y = 12 [resource A). x $ 8 (resource B), y s 6 (resource C). xy20 a. 16 b. 18 c. 20 d. 2210. What is the shadow price for the resource C constraint? Maximize z = x + 2y Subject to: x + y s 12 [resource A). x