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. Transportation. The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperones, and costs $ 1 , 200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $ 100 to rent. Since there are 400 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 400 students. Since only 36 parents have volunteered to serve as chaperones, the officers must plan to sue at most 36 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
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. Transportation. The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperones, and costs $ 1 , 200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $ 100 to rent. Since there are 400 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 400 students. Since only 36 parents have volunteered to serve as chaperones, the officers must plan to sue at most 36 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
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.
Transportation. The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport
40
students, requires
3
chaperones, and costs
$
1
,
200
to rent. Each van can transport
8
students, requires
1
chaperone, and costs
$
100
to rent. Since there are
400
students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least
400
students. Since only
36
parents have volunteered to serve as chaperones, the officers must plan to sue at most
36
chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
x
If f(x) =
=
L* f(t)dt
then find the value of ƒ (ln 7).
f: R R is continuous everywhere.
An eccentric, compressive 270-lb force P is applied to the end of a cantilever beam. Replace P with an equivalent force-couple system at G.
100 identical balls are rolling along a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximum number of collisions that can happen?
Let f(w) be a function of vector w Є RN, i.e. f(w) = 1+e Determine the first derivative and matrix of second derivatives off with respect to w.
Let A Є RN*N be a symmetric, positive definite matrix and bЄ RN a vector. If x ER, evaluate the integral Z(A,b) = e¯xAx+bx dx as a function of A and b.
John throws a fair die with faces labelled 1 to 6. ⚫ He gains 10 points if the die shows 1. ⚫ He gains 1 point if the die shows 2 or 4. • No points are allocated otherwise. Let X be the random variable describing John's gain at each throw. Determine the variance of X.
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