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Unformatted text preview: Name I See Math 110, EXAM 2A Mar 3 l, 2004 Show All Work! (1 7)_ ' 1.Graph the following system of linear equations on the grid below. Label each line with
ltS equation. Shade every discarded region. Clearly indicate the solution set with emphasized boundary and the letters F .R. 2x+3y$6 2x+y2 2 ys3 y22x For W “M; 2 J“ ‘20! draw
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; ?‘§2 (13)?“ Pictured below is the feasible region, FR, for a linear programming problem, r 7
(5)21. Find the coordinates of each vertex (corner point) 3 , '1 E V mt _ (add Verhces (2.3. AMA BQMSC)
baa:30 __ j) A=(89/24)) ~ 1’»? AP” 7L+U=W
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C $3,” m ®C= (0,39) ~ W t Find the minimum value of the objective function, 2 = 4x + 7y, on the region FR.
Show all work. (State All values of the objective function that are needed to ﬁnd the min.) Makl W @UwﬁgZA f“ [0% (got lmkh é [90 mg 44% a {M gadwé W Wdim S 25‘ MEI [mica 302(4),“10) E=([00,00)ﬁ2=(100,§)
equals , 2(C)=Séo ,2(0>=3290 ,¥(E)zl\00,2(F)=€¢%§ '1 pig 4 Calwhhwg “3(A32‘260 , ﬂ; Mgwm— (3 2(3): 2? 3mm d” I3 a vulex orgwwl FRt (14) 3. True/False (Circle the correct answer):
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T®a) If x_<_y anda<0, then x+a2y+a €610“ correc/i' QM‘ng @F b) If a linear programming problem in two unknowns has only one optimal
. solution, it must occur at a comer point. ® F c) Not every linear programming problem has an optimal solution. V
7 31:11:14; (Ci gﬁ ® F d) The empty set is a subset of every set. ., «a a
. a B ) W04: D 7 T®e) The intersection of two sets, A an s the set {x i xe A or xe B}. @ F 1) Ifn(A) = 11, n(B) = 12 and n(AuB) = 1s, n(AmB) = 5. T® g) If n(AxB) = 18 and n(B) '3 9 then n(A) = 9. (16) 4. Write a mathematical model for the following situation Clearly identify
variables, objective and constraints. DO NOT SOLVE THE MODEL. Cathy’s Catering delivers two types of luncheon buffets: standard and deluxe.
Each standard buffet requires 6 sandwich platters and 5 dessert displays while each
deluxe buffet requires 4 sandwich platters, 3 hot plates, and 6 dessert displays. Cathy has
45 sandwich platters, 20 hot plates and 56 dessert displays available. Due to demand,
Cathy must deliver at least 2 deluxe luncheon buffets and no more than twice as many
standard buffets as deluxe buffets. If the proﬁt on each standard buffet is $120 and the
proﬁt on each deluxe buﬁ‘et is $135, how many buﬂ’ets of each type should Cathy deliver
to maximize her proﬁt? My 1 1,M#=vi—simciwri~
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gpl’ ‘1 $ ‘Zpi‘ X?O ,‘37/0 (3) 5. List the elements in the set of outcomes of rolling two distinguishable dice such
that the numbers add to 6. 05) (2)0 (as) if) (250%) (9,2) m)
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cm Zl‘L 94‘ 3ft (3) In a state primary there are 54 candidates running for governor and 82 candidates
running for attorney general. What is the total number of possible outcomes? “(was MM Ms)
3’ 3 rt (6) 7.Your favorite ice cream shop offers a total of 25 ﬂavors. 15 of these ﬂavors have
chocolate as an ingredient and 17 have ﬁ'uit as an ingredient. Assuming that all of them
have either chocolate or fruit or both as an ingredient, how many have both? lit ntmcif
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l [or M9ka ‘lb 3 Pl: Mag): n(A)+m(6)~n(AUbizlS€l¥2§ : ¥ (9) 8. Let S denote the set of all gift baskets at Donna’s Dorm Treats and let: B = The set of her baskets that contain a beverage.
C = The set of her baskets that contain candy.
F = The set of her baskets that contain fruit. Using set notation (union, intersection, complement, etc), write each subset in
terms ofB, C, and F. a) The set of baskets that contain fruit or candy.
3?? ® F u C
b) The set of baskets that contain candy and a beverage.
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c) The set of baskets that contain fruit and candy but not a beverage. FnCnB' iy
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(@) 9. A survey of 100 showed that 15 owned CDs, 12 owned bonds, 14 owned stocks, 3 owned bonds and CDs, 5 owned stocks and CDs, 6 owned stocks and bonds
and 2 owned stocks, bonds and CDs. , (i b) a. . Solve the Venn diagram, where CD is the set of people who own CDs, B is
the set of people who own bonds and ST is the set of people who own stocks. 2% Q—g'Z. ZPT (he?) T) gal 2!” 44—55:) d=3 Zr!” was a 10:4 2;)?“ mgﬂiwziIS—A (1:9
210+ Quﬂwzil =9 (“35’ AtQKJLfSam rt‘) 2V? mgfcedearhgfheiwz) he?! (7;) b. How many people own no more than one of these types of investment? 5W HONOR PLEDGE: I pledge on my honor that I have not given or received any
unauthorized assistance on this examination or assignment.
Please write the exact wording of the pledge, followed by your signature, in the space below: ‘ Signature ...
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 Operations Research, Set Theory, Optimization, linear programming problem, Cathy

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