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 5-4 - C) x x x x4 z 5 4 B) x x x x4 z 5-4 - D) x x x x4 z 5 4
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 5 5 75 - - C) x x x x4 x5 z 5 5 75 B) x x x x4 x5 z 5 5 75 D) x x x x4 x5 z 5 5 75 - -
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)
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 4 5 5-9 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
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 x6 5 48 64 64 7 B) x x x x4 x5 x6 5 48 64 64-7 C) x x x x4 x5 x6 5 48 64 64-7 - D) x x x x4 x5 x6 5 48 64 64 - - 7 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
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
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) 9 9 9 9 ) 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
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
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