AMS 303 SECOND TEST REVIEW Solutions to Past Tests


Spring 2015 AMS 303 Second Test
1. x sub 10
2. a) digital sum of piles is 011=3, b) remove 3 from pile 3, c) take 1 from pile 3, d) g(0)=0, g(1)=1, g(2)=0, g(3)=1, g(4)=2, g(5)=3, g(6)=2, g(7)=0, sum is 10, remove 4 from pile 1.
3. a (-,oo), b(g-,1), c(h-,1), d(i-,1), e(j-,1), f(a+,1), g(c+) h(f+,1), i(f+,1), j(d+,1), k(d+,1), z(b+ or e+,1). One new solution b-k, c-g, d-i, e-j, f-h)
4.(1/8)[(b+w)^12 + 2(b^4+w^4)^3 + 3(b^2+w^2)^5 + 2(b+w)^2(b^2+w^2)^5].
5. Not possible,L & T play 4 games but they can collectively only win 3 games.
6. Initial solution: x11=30, x21=30, x22=20, x23=10, x33=20. Prices u1=$10, u2=$9, u3=$12, v1=$15, v2=14, v3=16. Select x13. Increase x13 and x21 by 10, reduce x11 and x23 by 10.
Spring 2013 AMS 303 Second Test
1. x sub 9.
2. a (-,oo), b(a+,1), c(j-,1), d(h-,1), e(i-,1), f(k-,1), g(e+ or f+,1) h(b+,1), i(c+,1), j(b+,1), k(d+,1), z(g+,1). One new solution b-j, c-i, d-h, e-g, f-k.
3. a) digital sum of piles is 011=3, b) remove 3 from pile 2 or 3, b) take 1 from pile 2, c) g(0)=0, g(1)=1, g(2)=2, g(3)=0, g(4)=1, g(5)=2, g(6)=0, g(7)=1, sum is 01, remove 1 from pile 3.

4.(1/4)[(b+w)^9 +(b+w)(b^2 + w^2)^4 +2(b+w)^3(b^2 + w^2)^3].
5. Not possible,L & T play 3 games but each can win only 1 game.
6. Initial solution: x11=40, x12=30, x22=10, x32=20, x33=40. Prices u1=$10, u2=$9, u3=$11, v1=v3=$15, v2=14. Select x13. Increase x13 and x32 by 30, reduce x12 and x33 by 30.

Fall 2012 AMS 303 Second Test (Test A)
1. (4 pt) x sub 8.
2. (15 pt) a (-,00), b(g-,1), c(h-,1), d (i-,1), e (a+,1), f (k-,1), g(e+,1), h(e+,1), i(b+,1), j(f+,1) or (d+,1), z(j+,1), one new matching b-i,c-h,d-j,e-g,f-k.
3. (15 pt- 2,3,3,7) a) 5, b) remove 3 from pile 2, or 5 from pile 3 or 4, c) remove 4 from piles 2,3, or 4, d) g(0)=0, g(1)=1, g(2)=0, g(3)=1, g(4)=2,g(5)=3, g(6)=2, g(7)=3, digit sum is 011-- remove 1 from pile 2, or 5 from piles 3 or 4.
4. (15 pt) (1/12)[(x1)^18 + 2(x6)^3 + 2(x3)^6 + (x2)^9 + 3(x1)^2*(x2)^8 + 3(x1)^4*(x2)^7].
5. (8 pt) Not possible-- 6 games to play but only supply of 5 wins.