桂林电子科技大学试卷
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一、Determine whether the following statements are true or not, and mark the letter ‘T ’ in the
bracket if the statement is true, or else mark the letter ‘F ’.（5420⨯=points ）
1. The convex set (){}
22,10D x y x y =+≤ has no extreme points. ( ) 2. The function ()222,,234f x y z x y z yz =---+ is concave. ( )
3. For linear programming problem, the dual is infeasible when the primal is unbounded. ( )
4. For the linear programming problem, any basic feasible solution is also an extreme point of
the feasible region. ( )
5. For the method of steepest descent, the two consecutive search directions are orthogonal
mutually. ( )
二、 Consider the following linear programming problem
12312341235236max 3..240220150,1,2,3
i S x x x s t x x x x x x x x x x x x i =++⎧⎪+++=⎪⎪+++=⎨⎪++=⎪⎪≥=⎩ It is known that 134,,x x x are optimal basic variables, write out the corresponding optimal simplex tableau.
(20 points)
三、 Use the dual simplex method to solve the following LP
()123123123min 234.. 23 234 0
S x x x s t x x x P x x x x =++⎧⎪++≥⎪⎨-+≥⎪⎪≥⎩
(20 points)
四、Let ()222123231232224662f x x x x x x x x x =+++++-+and assume ()f x can be
rewrited as ()1
2T f x x Ax bx c =++, T A A =, then
1. find out ,A b and c
2. evaluate ()f x ∇and ()2f x ∇
3. solve the problem ()min f x
（20 points ）
五、Use the steepest descend method to solve the following problem.
()()()2
2
1212min ,32f x x x x =-+-
Begin at the point 111x ⎛⎫
= ⎪⎝⎭ and the tolerance 0δ=.
（20 points ）