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Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. (2,5) (3.3) 29) 29) Objective Function: 2=X+9y+7 Find minimum A) minimum: 54 B) minimum: 38 C) minimum: 29 D) no minimum Graph the solution set of the system of inequalities or indicate that the system has no solution. 30) y>-3 30) x21 Write the partial fraction decomposition of the rational expression 822-8x+5 31) (x - 1) 31) (x - 1)2 (x - 1)3 DS (x - 1)2 (x-1 (x - 1)2 (x - 1)3 52.7x4 23.3x2.5x15 32) DS (x5) Solve the problem. 33) A store sells tents, sleeping bags and camp stools. A customer buys atent, 5 sleeping bags, and 233) camp stools for $231. The price of the tent is 7 times the cost of a camp stool. The cost of a sleeping bag is $21 more than the cost of a camp stool. Find the cost of each item A) 563 for a tent: $30 for a sleeping bag $10 for a camp stool B) 563 for a tent $35 for a sleeping bag 514 for a camp stoel C) 570 for a tent: $30 for a sleeping bag $10 for a camp stool D) 563 for a tent: $30 for a sleeping bag: $9 for a camp stool Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer 34) log(x+5).log(x-1)-2 34) A) -71 31 D) 13.-7

Answer 1

c (2,5) Sely (29) 5 3 23, 8(4,2) 2 2 3 4 Objective function : = +94 +7 0 minimum (2) min (7) = 3 + 9 (3)+7 (at A- (0,3) = 3 +27+ 7 = 37 ble Head At (B= (4,2)) min (2) = 4 + 9 (2) +7 4 +9(2) + 7 = 4 +18+7 = 129 At (e=(2,5)). 2+45+7 min (2) = 2 + 9 (5) +7 = 54 Here given LPP has minimum value at B= (4,2) th ( 29 < 37 < 54 29 C (30) Y-3, Hal AY - 8 2 H + -H -8 6 4 227 2 4 6 8 1-- -91

(B) (0) (B) is correct option. - 4 (31) 8 H² - 84 +5 (21-113 f(+1) Csay A C 8 4² 8x + 5 + -) + در 1- ) (4-1) (21-112 (214)3 Multiply bath ride by (21-1) 3 in ean (2) 82²-84+5 A (+1) + B. (2-1) + c 8x 84 +5 = A (2+1-24) - A (3P+1-24) + B (2-1) + -) → 8²-84 +5 A u²+ A-ZAM + Be-B + c - A-btc 5 Ә) ( constant terms) (terms in se terme in H²) -8 f - - 2A + B Р & 8 the matrine Now be written as rystem can 5. -8 (3) - FX = B -2 1 C 8

where -2 O 17 ㅋ variable (Matrix) 0 C o 3x3 (coefficient Matrix ) 5 B = Constant Motorise) -8 Augmented mature of system (3) ů [F/B] * Apply Rg 2R+ R₂ - -2 8 O -8 +8 Apply Rz ~ Rz – Ri 5. -1 al+2 -1 لا 0 Again apply Rg → Ret R3 Apply Rg Ag - 2 R3 -1 5 2 vrlo v - T Q 0 0 5 0 0 Again apply Rr R- Rz Apply Rgt - Rg 0 n -8 0 8 0 - 0 ایا O

Apply Rey Rita 0 20 0 5 A = 8, using naluer of get B = 8 & C=5 A, B & C in eah (2) then we 8 8 5 + t Hal 3 (4) 8 H²_84+5 (1) (Hall2 (22-1)3 Here egh (4) is the partial fraction de comporistion of the rational expression. C (1) is correct option. (32) 5x2+74+4 54² + H t 4 + 3 42 + 5x + 15 (3134 342) +(54415) 5H2 + 7x + 4 54²47244 212 (x+3) +5(3143) (3143) (22+5) - 2 = t 1+3 3 u-2 12+5 5 H2+7H + 4 3 + 3 H²+54 + 15 2 3x-2 1215 = ) 143 (2) (c) option is correct option.