(Goldilocks\' Mining 1) Goldilocks needs at least 12 lbs of gold and at least 18
ID: 3142026 • Letter: #
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(Goldilocks' Mining 1) Goldilocks needs at least 12 lbs of gold and at least 18 lbs of silver to pay the rent. There are two mines in which she can find gold and silver. Each day that Goldilocks spends in mine 1, she finds 3 lbs of gold and 1 lbs of silver. Each day that Goldilocks spends in mine 2, she finds 4 lb of gold and 2 lb of silver. Min X_1 + X_2 s.t. aX_1 + bX_2 greaterthanorequalto 12 (1) gold cX_1 + dX_2 greaterthanorequalto 18 (2) Silver X-1, X_2 greaterthanorequalto 0 In the LP above, the LHS coefficients are ___. a = 1, b = 3, c = 2, d = 4 a = 1, b = 2, c = 3, d = 4 a = 3, b = 4, c = 1, d = 2 a = 2, b = 1, c = 4, d = 3 Consider the LP maximization problem below max X + 4Y s.t. X lessthanorequalto 2 (1) X + 2Y lessthanorequalto 4 (2) X, Y greaterthanorequalto 0 The optimal objective value is ________. Z* = 2 Z* = 8 Z* = 4 Z* = 6 Consider the LP maximization problem below max X + 4Y s.t. X lessthanorequalto 2 (1) X + 2Y lessthanorequalto 4 (2) X, T greaterthanorequalto 0 With an optimal solution given, ___________ constraint (2) has a positive surplus constraint (1) has a positive surplus constraint (1) has a positive slack constraint (2) has a positive slackExplanation / Answer
Ans 7: total gold is to be >12 so 'a' and 'b' correspond to gold in X1 and X2 so a=3; b=4;
Similarly total silver is to be >18 so 'c' and 'd' correspond to silver in X1 and X2 c=1 ; d=2;
Hence the correct answer is option (c)
Ans 8: x<=2
x+ 2y<= 4
we have to maximise x+ 4y
we see here that y has a coefficient of 4 so we need ot assign maximum value to the variable 'y' ;
hence x=0 and 2y= 4 so y=2;
z= x+4y = 0+ 4*2 = 8;
Hence the maximum value of Z=8 ; Option (b) is the correct answer;
Ans 9 :
max x+ 4y so x= 0 and y=2;
constraint 1 is x<=2 which is true since 0<=2 so constraint 1 has a positive slack and constraint two is x+2y = 4 which is 0+2*2 = 4 which has neither slack nor suprlus so constraint 1 has a positive slack which means
option (c) is the correct answer;
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