Answer:
To complete the problem statement it is needed:
1.- the volume and weight capacity of the truck, because these will become the constraints.
2.- In order to formulate the objective function we need to have an expression like this:
" How many of each type of crated cargo should the company shipped to maximize profit".
Solution:
z(max) = 175 $
x = 1
y = 1
Assuming a weight constraint 700 pounds and
volume constraint 150 ft³ we can formulate an integer linear programming problem ( I don´t know if with that constraints such formulation will be feasible, but that is another thing)
Step-by-step explanation:
crated cargo A (x) volume 50 ft³ weigh 200 pounds
crated cargo B (y) volume 10 ft³ weigh 360 pounds
Constraints: Volume 150 ft³
50*x + 10*y ≤ 150
Weight contraint: 700 pounds
200*x + 360*y ≤ 700
general constraints
x ≥ 0 y ≥ 0 both integers
Final formulation:
Objective function:
z = 75*x + 100*y to maximize
Subject to:
50*x + 10*y ≤ 150
200*x + 360*y ≤ 700
x ≥ 0 y ≥ 0 integers
After 4 iterations with the on-line solver the solution
z(max) = 175 $
x = 1
y = 1
Answer:
Step-by-step explanation:
We are asked to find the slope of a line. The slope tells us the steepness and direction of a line. It is found by dividing the change in y by the change in x.
In this formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through. We are given the points (-6, 11) and (15,20). If we match a value with its corresponding variable, we see that:
- x₁ = -6
- y₁ = 11
- x₂ = 15
- y₂ = 20
Substitute the values into the formula.
Solve the numerator.
Solve the denominator. 2 back to back negative signs become a positive sign.
Simplify the fraction. 3 divides evenly into the numerator and denominator.
The slope of the line is <u>3/7.</u>
Part A
The first thing we must do for this case is to rewrite both expressions.
We have then:
1/2 (7x + 48) = (7/2) x + 24
- [1 / 2x - 3] + 4 (x + 5) = - (1/2) x + 3 + 4x + 20 = (7/2) x + 23
Answer:
We note that the first expression is greater than the second for all values of x.
Part B:
A new expression that is greater than both written expressions is:
(7/2) x + 25
For all values of x, this expression is always greater.
Answer:
(7/2) x + 25
Answer:
The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.
Step-by-step explanation:
The area of the parallelogram is given by the following expression:
The vectors are, respectively:
The base of the parallelogram is 8 units.
The height of the parallelogram is 3 units.
The cross product of both vectors is:
The area of the parallelogram is given by the norm of the resulting vector:
