Solve the minimization problem by using the simplex method to solve the dual problem.Minimize 24x1 + 16x2 + 30x3subject to 3x1 + x2 + 2x3 ? 50 x1 + x2 + 3x3 ? 35and x1 ? 0, x2 ? 0, x3 ? 0
A. Minimum = 510 when x1 = 
, x2 = 0, and x3 = 
B. Minimum = 498 when x1 = 12, x2 = 0, and x3 = 7
C. Minimum = 696 when x1 = 17, x2 = 18, and x3 = 0
D. Minimum = 
when x1 = 10, x2 = 
, and x3 = 
Answer: A
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Find the flux of the vector field F across the surface S in the indicated direction.F(x, y, z) = 11xi + 11yj + 11zk , S is the surface of the sphere x2 + y2 + z2 = 1 in the first octant, direction away from the origin
A. 
?
B. 0
C. 
?
D. 
?
The figure shows the percentage of the U.S. population, f(x), made up of teachersas a function of time, x, where x is the number of years after 1900. Use the graph to solve the problem. 
In which year did the percentage of teachers in the U.S. reach a minimum?
A. 2000 B. 1900 C. 1970 D. 1990
Use identities to simplify the expression. Do not use a calculator.2 cos275° - 1
A. - 
B. 
C. - 
D. 
Find a general term an for the geometric sequence.The first five terms of the sequence are 4, - 2, 1, - 
, 
.
A. an = 6 
n-1
B. an = 4 
n-1
C. an = 
n-1
D. an = 4 
n-1