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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- 1. Use simple fixed-point iteration to locate the root of f(x) = sin (√) - x Use an initial guess of xo = 0.5 and iterate until & ≤ 0.01%.arrow_forwardYou wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.arrow_forward4:using numpy to solve the system of linear equations as following x,y,z are variables. 3x+6y+7z = 10 2x+y+8y = 11 x+3y+7z = 22arrow_forward
- Evaluating and Solving Radical Functions A person's Body Mass Index is calculated with the formula: BMI=(weight / height2)⋅703 where weight is in pounds and height is in inches. If a person's BMI is above 25 and below 30, they are classified as overweight. If we solve this equation for height, we can determine how tall a person of a given weight should be if they have a BMI of 25.Our new Function is H(w)=√703w / b where H(w) is the person height in inches and ww is a person weight in pounds and b is the person's Body Mass Index (BMI). Use the function to answer the following questions. Determine how tall a person is if they weigh 225 pounds and they have a BMI of 25 Round your answer to one decimal place.The person that weights 225 pounds and has a BMI of 25 is about .......... inches tall. If a person is 68 inches tall and has a BMI of 25, determine their weight.A person that is 68 inches tall and has a BMI of 25 will weigh approximately ........... pounds.arrow_forward2. Find all values of x that satisfy both inequalities simultaneously for 10x – 7> 17 and 2x + 3 < 11. |arrow_forwardf(x) = sin (z*) %3D • Plot the function and a linear, quadratic and cubic Taylor series approximation about x=0 for x= 0 to 1.5 on the same plot. • Plot the function and a linear, quadratic and cubic Taylor series approximation about x=0.5 for x= 0 to 1.5 on the same plot.arrow_forward
- The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X2 X3 6 2 1 2 - 1 - 3 X1 1 3 -5 S₁ 1 0 0 S2 0 1 0 Z 0 0 1 18 39 The maximum is | when x₁ = ₁X₂ = ₁ x3 =₁ $₁=₁ and $₂ = - X3 (Type integers or simplified fractions.)arrow_forwardWhich option is correct for the following system equation? x-y-z=4 2x-2y-2z=8 5x - 5y - 5z = 20 answer a)Finite solutions b)No solution c)Subzero solutions d)Infinitely many solutions e)Unique solutionarrow_forwardusing Python/PuLP solve Turkeyco produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat. Cutlet 1 sells for $4/lb and must consist of at least 70% white meat. Cutlet 2 sells for $3/lb and must consist of at least 60% white meat. At most, 50 lb of cutlet 1 and 30 lb of cutlet 2 can be sold. The two types of turkey used to manufacture the cutlets are purchased from the GobbleGobble Turkey Farm. Each type 1 turkey costs $10 and yields 5 lb of white meat and 2 lb of dark meat. Each type 2 turkey costs $8 and yields 3 lb of white meat and 3 lb of dark meat. Part A: Formulate an LP to maximize Turkeyco’s profit. Part B: Solve the LP (provide exact values for all variables and the optimal objective function).arrow_forward
- Find the minimum of ƒ(x, y) = (y+3)² + (x − 2)² + (x y − 3)² Plot the function and display your solution. % Your code goes herearrow_forwardSuppose that the total cost (in dollars) for a product is given by C(x) = 1200 + 200 In(2x + 1) where x is the number of units produced. (a) Find the marginal cost MC function. MC = (b) Find the marginal cost when 200 units are produced. (Round your answer to the nearest cent.) Interpret your result. O The profit from the next unit will be approximately this amount. This is the total profit from producing 200 units. It will cost approximately this amount to make the next unit. O This is the total cost of producing 200 units. (c) Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function? O MC S0 O MC > 0 MC < 0 MC 2 0 MC = 0 %3D Does it apply in this problem? O Yes Noarrow_forwardSolve for x: 7x = 3 mod 11arrow_forward
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole