MATH 1300: Finite Mathematics EXAM 2 15 March 2017

Transcription

1 MATH 1300: Finit Mathmatics EXAM 2 15 March 2017 NAME:... SECTION:... INSTRUCTOR:... SCORE MC:(A) /12 * 7 = LA: /16 = Total: /100 = % INSTRUCTIONS 1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All xam pags must rmain stapld. Do not sparat or rmov any pags. You will hav 60 minuts to complt this xam. 2. This xam has 9 pags, including th covr sht. Thr ar 12 multipl choic qustions worth 7 points ach and 1 long answr qustion with six parts worth 16 total points. Only your scantron will b gradd for th multipl choic sction, what you put on your scantron is your FINAL answr. If you chang an answr on th scantron, ras your old answr thoroughly. 3. Blank grids for th multipl choic linar programming problms ar providd adjacnt to ach qustion. Thy ar providd for convninc only and will not b gradd. Th graph for th long answr qustion will b gradd.

2 MATH 1300 Spring 2017 Exam 2: Nam... (A) 2 MULTIPLE CHOICE: Mark your FINAL answrs on your scantron. Qustions 1-2: Kyl is choosing btwn a combination of brands of cat food to fd his cat. H dtrmins that th combination should mt crtain minimum nutritional rquirmnts: 36 units of protin, 35 units of fat, and 20 units of taurin pr wk. Brand A provids 4 units of protin, 7 units of fat, and 10 unit of taurin, and costs $3.50. Brand B provids 9 units of protin, 5 unit of fat, 2 units of taurin, and costs $4.00. Kyl wants to provid for his cat whil minimizing his total costs. Lt x b th numbr of cans of food A that h buys pr wk and y b th numbr of cans of food B. 1. Which of th following is an inquality associatd with this problm? a 10x + 2y 20 b 4x + 9y 36 c 7x 5y 35 d 3.5x + 4y 10 Non of th abov Which of th following is on of th vrtics of th fasibl st? a (9, 1) b (0, 4) c (0, 10) d (0, 9) Non of th abov

3 MATH 1300 Spring 2017 Exam 2: Nam... (A) 3 Qustions 3-4: An invstor has $18,000 to invst in thr typs of stocks, low-risk, mdium-risk and high-risk. Sh invsts according to thr principls. Th amount invstd in low-risk stocks will b at most $2000 mor than th amount invstd in mdium risk stocks. At last $8000 will b invstd in low-risk and mdium-risk stocks combind. At last $10,000 will b invstd in mdium-risk and high-risk stocks combind. Th xpctd yild for ths invstmnts ar 4% for low-risk stocks, 5.5% for mdium-risk stocks and 7.1% for high-risk stocks. Th invstor wishs to maximiz th yild on th invstmnts. Lt x b th amount to b invstd in low-risk stocks and y b th amount to b invstd in mdium-risk stocks. 3. Dtrmin th objctiv quation for this problm. a Maximiz Y =.04x +.055y + 18,000 b Maximiz Y = x.016y c Maximiz Y = 18, x.016y d Maximiz Y = x +.016y Non of th abov How much should th invstor invst in ach typ of stocks? a b c d $0 low-risk, $8000 mdium-risk, $10,000 high-risk $0 low-risk, $0 mdium-risk, $18,000 high-risk $5000 low-risk, $3000 mdium-risk, $10,000 high-risk $10,000 low-risk, $4000 mdium-risk, $4000 high-risk Non of th abov

4 MATH 1300 Spring 2017 Exam 2: Nam... (A) 4 5. If n(a) = n(a B), which of th following statmnts about A and B must b tru? a b c d A is a subst of B B = A B is a subst of A B A = Non of th abov 6. Lt U = {a, b, c, d,, f}, A = {d,, f}, B = {a, d, } and C = {a, c, d}. Which of th following is (A B) C? (A B) C = a {a, b, c, d,, f} b {a, d,, f} c {b, c} d {b} Non of th abov

5 MATH 1300 Spring 2017 Exam 2: Nam... (A) 5 7. If n(a B) = 42, n(a) = 100 and n(b) = 50, find n(a B). n(a B) = a 108 b 150 c 42 d 192 Non of th abov 8. Which of th following is th shadd rgion blow? R S T a R S T b (R S) T c (R S) T d R S T (R S) T

6 MATH 1300 Spring 2017 Exam 2: Nam... (A) 6 Qustions 9-10: A mrchant survyd 135 popl to dtrmin th way thy larnd about an upcoming sal. Th survy showd that 60 larnd about th sal from th radio, 80 from tlvision, 30 from th nwspapr, 20 from radio and tlvision, 15 from radio and nwspaprs, 10 from tlvision and nwspaprs, and 10 from all thr sourcs. 9. How many popl larnd of th sal from tlvision only? a 60 b 80 c 25 d 10 Non of th abov 10. How many popl larnd of th sal from both radio and tlvision? a 140 b 20 c 100 d 0 10

7 MATH 1300 Spring 2017 Exam 2: Nam... (A) Us D Morgan s Laws to simplify th xprssion (S T ). a S T b c S T S T d S T 12. Lt U = {Finit Math studnts this smstr}, A = {studnts who lik multipl choic qustions}, and B = {studnts who lik long answr qustions}. Dscrib th following st using st-thortic notation: {studnts who lik long answr qustions but not multipl choic qustions}. a A b c B A A B d A B Non of th abov

8 MATH 1300 Spring 2017 Exam 2: Nam... (A) 8 LONG ANSWER: Show complt work blow to rciv full crdit. Qustion 13: A coff roastr has warhouss in St. Louis and Topka and rcivs ordrs from coff shops in Kansas City and Columbia. Th St. Louis warhous has 500 lbs of coff and th Topka warhous has 700 lbs of coff. Th Kansas City coff shop rqusts 400 lbs and th Columbia stor 350 lbs. Th cost of shipping from St. Louis to Kansas City is $4 pr pound and St. Louis to Columbia is $2 pr pound. Th cost of shipping from Topka to Kansas City is $2.50 pr pound and th cost of shipping from Topka to Columbia is $3 pr pound. Lt (x, y) corrspond to x pounds of coff shippd from St. Louis to Columbia and y pounds of coff shippd from St. Louis to Kansas City. Th coff roastr wishs to find th (x, y) that minimizs th company s th shipping costs. a) Writ th st of six inqualitis that (x, y) must satisfy b) Writ th objctiv quation c) Us th grid providd to graph th fasibl st. d) Idntify th vrtics of th fasibl st.

9 MATH 1300 Spring 2017 Exam 2: Nam... (A) 9 ) Which valus for x and y minimiz th cost of fulfilling th ordr? f) How much coff should thn b shippd from Topka to Columbia?