An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.
The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.
Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.
Which expression is equivalent to:
25a + 5b - 13
Answer:
The correct option is 4.
Step-by-step explanation:
The given expression is
[tex]25a+5b-13[/tex]
In option (1), the given expression is
[tex]20a+5a+b-13[/tex]
Combine like terms.
[tex]25a+b-13[/tex]
This expression is not equivalent to the given expression.
In option (2), the given expression is
[tex]20(5a+5b)-13[/tex]
Using distributive property.
[tex]100a+100b-13[/tex]
This expression is not equivalent to the given expression.
In option (3), the given expression is
[tex]30ab-13[/tex]
This expression is not equivalent to the given expression.
In option (4), the given expression is
[tex]5(5a+b)-13[/tex]
Using distributive property.
[tex]25a+5b-13[/tex]
This expression is equivalent to the given expression.
Therefore correct option is 4.
3x - 12 + 6x + 9?/ Help Please
Write an equation that represents the data in the table x 5,10,15,20 y 17,22,27,32
ashley measure the shell she collect she records the measurements in the chart
You are due a $750 paycheck at the end of the week (Friday), but want to get your hands on the cash on Monday. A payday lender offers to make this deal with you for a fee of 2% of the paycheck. What is the rate you are paying for this service? Assume a 365-day year.
A cake decorator rolls a piece of stiff paper to form a cone. She cuts off the tip of the cone and uses it as a funnel to pour decorative sprinkles into small containers. The cone has a radius of 666 cm and a height of 181818 cm. What is the volume of the cone before the end is cut off? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer:
V = 216 pi cm^3.
Step-by-step explanation:
Choose the right answer. Two hundred fifty tickets are sold at a church fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is .
Answer:
Her probability to win the prize quilt is 0.06, or she has a 6% probability of winning it.
Step-by-step explanation:
In statistics, a probability of 100% is represented with a 1. In this case, if Sarah would have bought the 250 tickets, she would have a probability of 1 to win the prize, as
[tex]\frac{250}{250}=1[/tex]
then, if this expression is multiplied by 100, we could say that the precentage of probability would have been 100%...
But Sarah didn't buy the 250 tickets, instead she bought 15, therefore
[tex]\frac{15}{250}=\frac{3}{50}=0.06[/tex]
which means that the probability of her winning the prize quilt is 0.06, or, if multiplied by 100, she has a 6% probability of winning the prize quilt.
A scale drawn on the map shows that 1 inch represents 24 miles. Of two cities are 2.25 inches apart on the map, what is the distance between them in real life?
For her cell phone plan Heather pays $30 per month plus 0.05 protects she wants to keep her bill under $60 per month with any quality represents the number of texts T Heather can't spend each month while staying within her budget
Prepare 350g of a 2% lidocaine cream using a 1% lidocaine cream a 5% lidocaine cream
the initial population was 50 thousand people and the population increased by 12% each year. Determine the function rule for this definition.
Jane goes to the fruit market every week. On Monday she buys 10 pears and 11 oranges for $10.05 By Friday she is out of fruit and goes back to the market to purchase 1 pear and one orange for $0.94 How much did Jane spend on 1 orange?
Jackie has a drawer with 20 buttons, each of different color. How many different ways can she choose three buttons for her bookbag?
15% of the school parking spaces are handicap spaces. The school has 18 handicap spaces. How many parking spaces are there?
Answer:
The answer is "120"
Step-by-step explanation:
I did it myself, and this is the answer i got :) I made sure it was correct but let me know if you have problems!
here goes another question lol oops
gloria went to the mall and spent 50 minutes shopping. then she. had lunch for 30 minutes. if gloria arrived at the mall at 11:00 a.m at what time did she finished lunch?
Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?
Convert 15/9 to a decimal. A. 1.64 B. 1.67 C. 1.66 D, 1.69
Which of the following is parallel to the line =6x + 1
how do u estimate 8.36
What is the area of a triangle that has a base of 15 1/4 in and a height of 18 in?
The area of the triangle is half the product of its base and height. The area of the triangle is 137.25 in².
What is the area of the triangle?The area of the triangle is half the product of its base and height. It is given by the formula,
[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]
As it is given that the base of the triangle is 15¹/₄ inches, while the height of the triangle is 18 inches. Therefore, the area of the triangle is,
[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]
[tex]= \dfrac{1}{2} \times 15(1/4)\times 18\\\\\\ = \dfrac{1}{2} \times \dfrac{(15\times 4)+1}{4} \times 18\\\\\\= \dfrac{1}{2} \times \dfrac{61}{4} \times 18\\\\\\=137.25\rm\ in^2[/tex]
Hence, the area of the triangle is 137.25 in².
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convert 82 into a fraction and decimal
A basketball player made 57 out of 100 attempted free throws. What percent of free throws was made?
Using an algebraic rule, describe a translation 2 units to the left.
Can someone please help me? The measure of the reflex angle in rhombus ABCD is 260°. Find x. Thanks
The ratio of french fries to packets of ketchup in Philip's bag is 8:1. What does this mean? A. There are 7 more french fries than packets of ketchup. B. For every 8 french fries, there is 1 packet of ketchup. C. For every 8 packets of ketchup, there is 1 french fry. D. There are 8 more french fries than packets of ketchup.
Granny has some stickers.if she gives 6 stickers to each of her grandchildren,she will have 5 stickers left.if she gives 7 stickers to each of her grandchildren,she will need 2 more stickers.how many grandchildren does granny have?
the width of a rectangle is X and the length is twice he width. if the area of the rectangle is 162, what is X?
To find the value of X in a rectangle with width X and length 2X, we can use the area formula. By solving the equation, we find X = 9, making the width of the rectangle 9 units.
Explanation:To find the value of X, we need to use the given information about the length and width of the rectangle. Let's assume the width of the rectangle is X. Since the length is double the width, it is 2X. The area of the rectangle is given as 162, so we can set up the equation:
Width × Length = Area
X × 2X = 162
Simplifying the equation, we get:
2X^2 = 162
Dividing both sides by 2, we have:
X^2 = 81
Taking the square root of both sides, we find:
X = ±9
Since the width cannot be negative, the value of X is 9. Therefore, the width of the rectangle is 9 units.
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The width of the rectangle is 9 units.
Explanation:To find the width of the rectangle, we can set up the equation for the area. The width of the rectangle is X, and the length is twice the width, meaning the length is 2X. The formula for the area is length times width, so we have X * 2X = 162. Simplifying this equation gives us 2X^2 = 162. Dividing both sides by 2 gives us X^2 = 81. Taking the square root of both sides gives us X = 9. Therefore, the width of the rectangle is 9 units.
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I need help!!! Pleasssse!!!!
The ratio of the length to the width to the height of a rectangular box of cereal is 6:2:7. The sum of the length and the width of the box is 24 centimeters. Find the surface area of the box of cereal
which of these equations represents functions? check all that apply
Trig: Use a half angle formula to find the exact value of the expression?
cos(5pi/12)
The correct answer is [tex]\frac{1}{2}[/tex].
To find the exact value of [tex]\cos(5\pi/12)[/tex] using a half-angle formula, we can follow these steps:
[tex]\cos(2\theta) = 2\cos^2(\theta/2) - 1[/tex]
Substituting [tex]\theta = 5\pi/6[/tex], we get:
[tex]\cos(5\pi/3) = 2\cos^2(5\pi/12) - 1[/tex]
[tex]\cos^2(5\pi/12) = \frac{\cos(5\pi/3) + 1}{2}[/tex]
[tex]\cos(5\pi/3) = \cos(\pi/3 + \pi) = -\cos(\pi/3)[/tex]
[tex]\cos(\pi/3) = \frac{1}{2}[/tex]
[tex]\cos(5\pi/3) = -\frac{1}{2}[/tex]
[tex]\cos^2(5\pi/12) = \frac{-\frac{1}{2} + 1}{2} = \frac{1}{4}[/tex]
[tex]\cos(5\pi/12) = \pm\sqrt{\frac{1}{4}} = \pm\frac{1}{2}[/tex]
Since cosine is an even function, we take the positive value.
[tex]\cos(5\pi/12) = \frac{1}{2}[/tex]
Therefore, the exact value of [tex]\cos(5\pi/12)$ is $\frac{1}{2}[/tex].
Complete question:
Use a half angle formula to find the exact value of the expression?
[tex]\cos(5\pi/12)[/tex]