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# Optimization

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### Optimization Modeling In Excel (using Solver)

A marketing research group needs to contact at least 150 wives, 120 husbands, 100 single adult males, and 110 single adult females. It costs \$2 to make a daytime call and (b/c of higher labor costs) \$5 to make an evening call. Because of the limited staff, at most half of all phone calls can be evening calls. Determine how to

### Appropriate Quantitative Forecasting Methods

What conditions make quantitative forecasting methods appropriate? Besides taking historical data to forecast future data points. Please provide an explanation without using math if possible.

### Staffing optimization can offer significant cost savings to your company

Have you ever run a company? Do you know that companies face staffing schedule optimization problems everyday? The following problem relates to a conventional staffing optimization problem. You will find that when you know about optimization, your company could identify significant cost-savings strategies. In this example, you'l

### Maintenance at a major theme park in central Florida

Maintenance at a major theme park in central Florida is an ongoing process that occurs 24 hours a day. Because it is a long drive from most residential areas to the park, employees do not like to work shifts of fewer than eight hours. These 8-hour shifts start every four hours throughout the day. The number of maintenance worker

### Optimization Problems : Largest Rectangle in a Semicircle

Find the area of the largest rectangle that can be inscribed in a semicircle of radius r. A can in the shape of a right circular cylinder is to be made to hold 1 L of oil. Find the dimensions of the can that will minimize the cost of the metal to manufacture the can. Find the point on the parabola y^2 = 2x that is clo

### Finding the Minimum Distance Between Two Objects

Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?

### Interpreting LINDO output in linear programming optimization

Based on the attached file, please anwer: a. Give the complete optimal solution b. What constraints are binding? c. What would happen if the coefficient of X1 is increased by 6? d. What would happen if the right-hand-side value of constraint 1 decreased by 10? e. Which right-hand-side would you be most intereste

### Interpreting LINDO Output in Linear Programming Optimization

Based on the attached file, please anwer: a. Give the complete optimal solution b. What constraints are binding? c. What is the dual price for the second constraint? d. Over what range can the objective function coefficient X2 vary before a new solution point becomes optimal? e. What would happen if the first constra

### Rate of return and interest problems

Calculate ROR.... (see attachment for full questions) I need to get some outline on a step by step method to solve the problem(s). Some of them involve optimisation.

### Applied differentation/optimization

It may be the mental picture that's confusing me, but I can't figure this one out: "A painting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an observer. How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand

### Calculating Maximum and Minimum Distance travelled

A car travels at a constant speed of 70km per hour for a time of 2 hours and 45 minutes. Its speed is quoted to the nearest km/h and the time is quoted to the nearest minute. Calculate: a) the maximum possible distance that the car could have travelled b) the minimum distance the car could have travelled

### Research Works for Satellite Route Optimization.

The Satellite Mission Scheduling problem with Dynamic Tasking (SMS-DT) involves scheduling tasks for a satellite, where new task requests can arrive at any time, non-deterministically, and must be scheduled in real-time. The schedule is a time ordered sequence of activities (scheduled tasks) to be performed by the payload of a s

### Increase, Decrease, Extrema, Concavity, Inflection Points

F(x)=ln((x^4)+27) (a)Find the intervals of increase and decrease. (b)Find the local maximum and minimum values. (c)Find the intervals of concavity and inflection points. (d)Use the information from (a)-(c) to sketch the graph.

### Determining the Minimum of Closed, Continuous Analytic Function

4. Let a function f be continuous in a closed bounded region R, and let it be analytic and not constant throughout the interior of R. Assuming that f(z) does not equal 0 anywhere in R, prove that f(z)f has a minimum value n in R which occurs on the boundary of R and never in the interior. Do this by applying the corresponding re

### Critical Points (Local Maximum, Local Minimum, Saddle Points)

(a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f = 0) (b) Classify the critical point of f as local maximum, local minimum or saddle points. See the attached file.

### Functions : Continuity, Increasing/Decreasing, Maxima and Minima

1. Determine where the function f(x)= 1/(x^2-x) is continuous. (See attachment for full questions)

### Locate Maxima and Minima on a Closed Interval

Locate all relative (local) and absolute maxima and minima for the function: f(x)=2x^5-5x^4+7 on the closed interval [-1,3/2].

### Function on a Closed Interval : Local Maxima and Minima

Consider the following function f(x)=2sinx-cos2x on the closed interval [0,2pi]. Task: Find all relative (local) and absolute maxima and minima for the function listed above.

### Local and Absolute Maxima and Minima

Locate all relative (local) and absolute maxima and minima for the function: f(x) = x^2/x^2+1 over the entire graph (negative infinity, positive infinity).

### Optimization - Dimensions

A customer has asked me to design an open-top stainless steel vat. It is to have a square base and a volume of 32 cubic ft. to be welded from quarter-inch plate, and to weigh no more than necessary. What dimensions do I recommend?

### Maximize Demand for Base Length and Volume

The area of a closed box is 200 square inches. If the box has a square base, find the length of the base that will maximize the volume.

### Optimization for trapezoid

A trough with trapezoidal cross sections is formed by turning up the edges of a 30 inch wide sheet of aluminum. Find the cross section of maximum area. (See Attachment for details)

### Minimization and contour point

Consider the minimization of *see attached for equation* subject to the constraint of *see attached for equation* (a) Graph the contour point of with y-axis and x-axis between -2 and 6.(on my paper there is a dot (between point (3,3) Estimate where extrema values may occur and compute the function values correspondi

### Critical Points, Max-Min values, inflection points

Given: y = f(x) = 3x4 + 4x3 Find: A. All critical points B. Max - Min Values C. Inflection points D. Where is f(x) concave up E. Where is f(x) concave down F. X and Y intercepts G. Where f(x) is increasing H. Where f(x) is decreasing I. Sketch the curve label

### Optimization of business and economics

A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to have 1.5 inches, and the margins on the left and right are to be in 1 inch. What should the dimensions of the page be so that the least amount of paper is used?

### Optimization Total Area of Squares

A wire 10 feet long is to be cut into two pieces, each of which is to formed into a square. What is the largest possible total area of the two squares? What is the smallest possible total area?

### Random Number Generator

For the equation RAND = (ac+m)MOD MAX , if the set of random numbers is known, is it possible to calculate a,c and m?

### dynamic programming function

This spring I want to plant a garden on a 10x20 feet of land. The rows are each 10 feet long. I want to plant tomatoes, corn and green beans. The corn and tomatoes rows will be 2 feet wide each. The green beans will each be 3 feet wide. On a scale of 1 to 10 (10 being the best) I would place tomatoes at 10, corn at 7, and b

### Dynamic Programming - The Allocation Problem

Please see the attached file for the fully formatted problems. The beginning appears below... Example Problem: A sales manager has 3 areas and 5 sales engineers. If the assignment of sales engineers to areas will result in the expected sales as shown, how should the engineers be assigned to maximize sales?

### Maximum

Please see the attached PDF file. Thanks! I would like someone other than OTA#103746 or 101620 to attempt a solution.