In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method. Refer to Problem 53. If each van can transport 7 people and there are 35 available chaperones, show that the optimal solution found graphically involves decimals. Find all feasible solutions with integer coordinates and identify the one that minimizes the transportation costs. Can this optimal integer solution be obtained by rounding the optimal decimal solution? Explain.
In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method. Refer to Problem 53. If each van can transport 7 people and there are 35 available chaperones, show that the optimal solution found graphically involves decimals. Find all feasible solutions with integer coordinates and identify the one that minimizes the transportation costs. Can this optimal integer solution be obtained by rounding the optimal decimal solution? Explain.
In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.
Refer to Problem 53. If each van can transport
7
people and there are
35
available chaperones, show that the optimal solution found graphically involves decimals. Find all feasible solutions with integer coordinates and identify the one that minimizes the transportation costs. Can this optimal integer solution be obtained by rounding the optimal decimal solution? Explain.
4.
Prove: If x {0, 1} then x² -
-x=0.
5.
6.
Prove by contrapositive: Suppose x is a real number. If x>0 then x + 16 0.
Prove by contradiction: Suppose n is an integer. Then n² - n+10.
Hint: You might try organizing the proof by cases on whether n is even or odd. Is n² - n+1 even or odd?
Let f(x)=7x²-2x and g(x) = 5x+3. Find f[g(k)].
Use the method of reduction of order to find a second solution to
ty"-(4t+4)+(4t+8)y = 0, t> 0
Given y₁(t) = e²t
Y2(t) =
Give your answer in simplest form (ie no coefficients)
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