Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
Working conditions in the United States in the early 1900’s can best be described as atrocious.
The graph that shows the solution to the system of inequalities is: C (see the image attached below).
<h3>How to Determine the Graph of the Solution to a
System of Inequalities?</h3>
Given the following systems of inequalities:
y < -1/3x + 1
y ≤ 2x - 3
Below are the features of the graph that represents a solution to the system of inequalities:
- The boundary line of y < -1/3x + 1 would be a dashed line and the shaded area would be below it, because of the inequality sign, "<".
- The boundary lines of y ≤ 2x - 3 would be a solid line and the shaded area would be below it, because of the inequality sign, "≤".
- The slope of the shaded line that represents y < -1/3x + 1, would be -1/3, and the line would be a decreasing line which intersects the y-axis at 1.
- The slope of the line that represents y ≤ 2x - 3, would be 2, and the line would also be an increasing line that intersects the y-axis at -3.
Therefore, the graph that shows the solution to the system of inequalities is: C (see the image attached below).
Learn more about the graph of the system of inequalities on:
brainly.com/question/10694672
#SPJ1
Answer:
Step-by-step explanation:
f(x) = 1/2(4)^x
Plug in 3 for x
f(3) = 1/2(4)³
Cube 4.
4³ = 4 x 4 x 4 = 64
f(3) = 1/2(64)
Multiply 64 with 1/2 (or divide by 2)
f(3) = 64/2
f(3) = 32