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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function: S = 35L0.40 0.60 In this formula L represents the units of labor Input and C the units of capital input. Each unit of labor costs $150, and each unit of capital costs $200. a. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. If the constant is "1" it must be entered in the box; if your answer is zero, enter "0". Min s.t. L C L, C b. Solve the optimization problem you formulated in part (a). Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5000 for both L and C before solving. Round your answers for L and C to three decimal places. Round your answer for optimal solution to one decimal place. L= and C= for an optimal solution of $. Please do…arrow_forward1. 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_forward
- Solve the following using deetailed explanationarrow_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_forward2. Find all values of x that satisfy both inequalities simultaneously for 10x – 7> 17 and 2x + 3 < 11. |arrow_forward
- Solve for x: 7x = 3 mod 11arrow_forwardThe 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_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
- 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_forwardThe following table belongs to the optimal solition nit of a Lineer Programming Problem. Obtain the formulation of the initial problem. XI x2 ke -Jig 38 X₁ Xu O 1 O 19 41 14 23 38 xu O O 1 VI 38 A 38 AL A2 (1-38M) (2-19M) 38 19 -3 38 5 L 응급 31 19 19 solution 7' 2 5arrow_forwardplease solve in a quarter of an hour and they came An electricity distribution company wants to calculate the electricity fee to be paid by the subscriber according to the type of electricity usage place (Residential: u or U, Workplace: p or P) as follows; In workplaces; 3.78TL for each kilowatt-hour (kwh), In residences Up to the first 60 kWh, each kWh is 2.98 TL, Then, up to 120 kWh, each kWh is 3.62 TL, For more (more than 100 kWh), it charges 2.56 TL for each kWh. Using the C programming language, write an electricity bill calculation program in accordance with the rules below. 1-Use the switch.case structure while writing the program. 2-First, we ask the user for the 6-digit subscriber number. The user will enter a random 6-digit number after the program runs. 3- After entering the usage type, the first and last meter reading values will be entered randomly from the keyboard. Here, the first read value cannot be greater than the last read value. Create a blocking line for this…arrow_forward
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole