MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Size: px

Start display at page:

Download "MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question."

Brett Lewis
5 years ago
Views:

1 Math 4 review exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the constraints into linear equations by using slack variables. ) Maximize z =.x +.6x Subject to:.9x +.5x 6.6x +.x 9 x, x A).9x +.5x + x 6.6x +.x + x4 9 C).9x +.5x + x = 6.6x +.x + x = 9 B).9x +.5x + x = 6.6x +.x + x4 = 9 D).9x +.5x = x + 6.6x +.x = x4 + 9 ) ) Maximize z = x + 5x Subject to: 5x + 7x x + 4x 4 x, x A) 5x + 7x + x x + 4x + x4 4 C) 5x + 7x + x = x + 4x + x4 = 4 B) 5x + 7x = x + x + 4x = x4 + 4 D) 5x + 7x + x = x + 4x + x = 4 ) Introduce slack variables as necessary and write the initial simplex tableau for the problem. ) Maximize z = 4x + x subject to: x + 5x x + x x, x ) A) x x x x4 z C) x x x x4 z 5 4 B) x x x x4 z D) x x x x4 z 5 4

2 4) Maximize z = x + x subject to: x + x x + x x + x x, x > 4) A) x x x x4 x5 z C) x x x x4 x5 z - - B) x x x x4 x5 z - - D) x x x x4 x5 z 5) Maximize z = x + x subject to: x + x 5 x + x 5 x + x 75 x, x > 5) A) x x x x4 x5 z C) x x x x4 x5 z B) x x x x4 x5 z D) x x x x4 x5 z

3 Find the pivot in the tableau. 6) 6) A) in row, column B) 4 in row, column C) in row, column D) 4 in row, column 7) 7) A) 4 in row, column B) in row, column 5 C) in row, column D) 9 in row, column Use the indicated entry as the pivot and perform the pivoting once. 8) 8) A) B) C) D)

4 9) 9) A) B) C) D) Write the basic solution for the simplex tableau determined by setting the nonbasic variables equal to. ) x x x x4 x5 z A) x = 5, x =, x =, x4 =, x5 =, z = B) x =, x = -, x =, x4 =, x5 =, z = C) x = 5, x =, x =, x4 =, x5 =, z = 9 D) x = 5, x =, x =, x4 =, x5 =, z = 9 ) 4

5 Use the simplex method to solve the linear programming problem. ) Maximize z = 5x + x subject to: x + 4x x + x 6 with x, x A) Maximum is 8 when x =, x = 6 B) Maximum is when x = 6, x = C) Maximum is 9 when x =, x = D) Maximum is.5 when x = 6.5, x = ) A bakery makes sweet rolls and donuts. A batch of sweet rolls requires lb of flour, dozen eggs, and lb of sugar. A batch of donuts requires 5 lb of flour, dozen eggs, and lb of sugar. Set up an initial simplex tableau to maximize profit. ) The bakery has 48 lb of flour, 64 dozen eggs, 64 lb of sugar. The profit on a batch of sweet ) rolls is $7. and on a batch of donuts is $.. A) x x x x4 x5 x B) x x x x4 x5 x C) x x x x4 x5 x D) x x x x4 x5 x A manufacturing company wants to maximize profits on products A, B, and C. The profit margin is $ for A, $6 for B, and $5 for C. The production requirements and departmental capacities are as follows: Department Production requirement by product (hours) Departmental capacity (Total hours) A B C Assembling, Painting 8, Finishing 8, ) What are the coefficients of the objective function? ) A),, B),, C), 6, 5 D),, 4) What are the constants in the model? A),, B), 6, 5 C),, 8,, 8, D),, 4) 5

6 5) What is the constraint for the assembling department? A) A + B + C, B) A + B + C, C) A + B + B 8, D) A + B + C 8, 5) TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false. Tell whether the statement is true or false. 6) {x x is a counting number greater than 6} = {6, 7, 8,... } 6) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Insert ʺ ʺ or ʺ ʺ in the blank to make the statement true. 7) {a, d, j, i} {a, d, j, i, n} A) B) 7) 8) {x x is a counting number larger than 5} {7, 8, 9,... } A) B) 8) Find the number of subsets of the set. 9) {x x is a day of the week} A) 56 B) 4 C) 8 D) 7 9) TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false. Decide whether the statement is true or false. ) {4, 6, 8} {5, 7, 9} = {4, 6, 8, 5, 7, 9} ) ) {, 6, 9, } {, 9} = {, 6, 9, } ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated set, using set braces. ) A Bʹ ) A) {r, s, t, u, v, w, x, z} B) {t, v, x} C) {u, w} D) {q, s, t, u, v, w, x, y} ) (A B)ʹ A) {t, v, x} B) {r, t, u, v, w, x, z} C) {s, u, w} D) {q, s, t, u, v, w, x, y} ) 4) (A B)ʹ A) {t, v, x} B) {r, s, t, u, v, w, x, z} C) {s, u, w} D) {r, t, v, x} 4) 5) Cʹ Aʹ A) {w, y} B) {q, s, u, v, w, x, y, z} C) {r, t} D) {q, r, s, t, u, v, x, z} 5) 6

7 Write the sample space for the given experiment. 6) An 8-sided die is rolled. (The sides contain the numbers,,, 4, 5, 6, 7, and 8.) A) {64} B) {8} C) {, 8} D) {,,, 4, 5, 6, 7, 8} 6) 7) A box contains blue cards numbered through, and green cards numbered through. A blue card is picked, followed by a green card. A) {7} B) {(, ), (, ), (, ), (, ), (, ), (, )} C) {(, ), (, ), (, ), (, ), (, ), (, )} D) {} 7) For the experiment described, write the indicated event in set notation. 8) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The first toss shows a six. A) {(6, )} B) {(6, ), (6, ), (6, ), (6, 4), (6, 5), (6, 6)} C) {(6, ), (6, ), (6, 5)} D) {(6, ), (6, ), (6, 4), (6, 5), (6, 6)} 8) 9) A coin is tossed three times. Represent the event ʺthe first toss comes up tailsʺ as a subset of the sample space. A) {tails, heads, heads} B) {thh, tht, tth, ttt} C) {thh, tht, tth} D) {hhh, hht, hth, htt, thh, tht, tth, ttt} 9) Find the probability of the given event. ) A card drawn from a well-shuffled deck of 5 cards is a red ace. ) A) B) C) 5 D) 6 ) A card drawn from a well-shuffled deck of 5 cards is an ace or a 9. A) B) 5 C) D) ) ) A bag contains 5 red marbles, 9 blue marbles, and green marbles. A randomly drawn marble is blue. ) A) 9 6 B) 9 4 C) 8 D) 5 6 ) A bag contains 9 balls numbered through 9. A randomly chosen ball has an even number. A) B) 9 C) 9 D) ) Solve the problem. 4) A single die is rolled one time. Find the probability of rolling an odd number or a number less than 5. 4) A) B) 5 6 C) D) 7

8 Suppose P(C) =.48, P(M C) =.44, and P(M C) =.54. Find the indicated probability. 5) P(M) A).58 B).47 C).48 D).5 5) Find the odds in favor of the indicated event. 6) Spinning an A on the spinner pictured below. (The sectors are of equal size.) 6) A) to B) to 5 C) to D) to 8

9 Answer Key Testname: REVIEW FALL 5 ) B ) C ) A 4) B 5) A 6) B 7) D 8) D 9) B ) C ) B ) C ) C 4) C 5) B 6) FALSE 7) A 8) A 9) C ) FALSE ) TRUE ) C ) B 4) D 5) C 6) D 7) B 8) B 9) B ) D ) D ) A ) D 4) B 5) D 6) B 9

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Math324 - Test Review 2 - Fall 206 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the vertex of the parabola. ) f(x) = x 2-0x + 33 ) (0,