Problems 25-32 are mixed. Some can be solved by the methods presented in Sections 6.2 and 6.3 while others must be solved by the big M method. Maximize P = 7 x 1 − 5 x 2 + 2 x 3 subject to x 1 − 2 x 2 + x 3 ≥ − 8 x 1 − x 2 + x 3 ≤ 10 x 1 , x 2 , x 3 ≥ 0
Problems 25-32 are mixed. Some can be solved by the methods presented in Sections 6.2 and 6.3 while others must be solved by the big M method. Maximize P = 7 x 1 − 5 x 2 + 2 x 3 subject to x 1 − 2 x 2 + x 3 ≥ − 8 x 1 − x 2 + x 3 ≤ 10 x 1 , x 2 , x 3 ≥ 0
Solution Summary: The author calculates the solution of the linear programming problem by using the big M method.
The function f is shown below. If g is an antiderivative of f such that g(6) = 2, what is the maximum value of g on the closed interval
[-9,9]?
8
7
6
Сл
5
4
3
1
y
Graph of f
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
23 4
-1
-2
-3
-4
-6
56
-5
-7
-8
LO
5
9
7
8
9
10
x
The function of is shown below. If I is the function defined by g(x) = [* f(t)dt, write the equation of the line tangent to the graph of 9
at x = -3.
g
y
Graph of f
8
7
6
5
4
32
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2
3 4
5
6
7
8
9 10
-1
-2
-3
56
-6
-7
-8
-
Problem 3: For a short time, the 300-kg roller-coaster car with passengers is traveling along
the spiral track at a constant speed of v = 8 m/s with r = 15 m. If the track descends d =
6 m for every full revolution, 0 = 2π rad, determine the magnitudes of the components of
force which the track exerts on the car in the r, 0, and z directions. Neglect the size of the car.
Bonus: Develop a MATLAB program to solve for this problem.
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