In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
- a. Graph the system of inequalities representing the constraints.
- b. Find the value of the objective function at each corner of the graphed region.
- c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
7. Objective Function Constraints
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- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardFind the maximum value of P=4x+3y subject to the constraints of Example 1. {x+y42x+y6x0y0arrow_forwardA company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day.a. Draw the graph that represents the constraint inequalities. Choose the correct corner points. A. (150,50),(200,0),(300,0) B. (0,200),(150,50),(300,0) C. (0,100), (150,50), (200,0), (0,0) D. (0,100),(150,50),(0,200) c. Maximize the revenue the trimmers with the electric trimmers costing $9 and cordless trimmers costing $13. How many of each trimmer must be sold? A. Revenue of $1,300 with no electric trimmers and 100 cord-less trimmers. B. Revenue of $2,000 with 150 electric trimmers and 50 cord-less trimmers. C. Revenue of $2,700 with 300 electric trimmers and no cord-less trimmers. D. Revenue of $1,800 with 200 electric trimmers and no cord-less trimmers.arrow_forward
- Part 3: Linear Programing 1. Graph the following system of linear inequalities: yarrow_forwardDetermine the number of slack variables and name them. Then use the slack variables to convert each constraint into a linear equation. How many and which slack variables should be assigned? OA. There are three slack variables named x₁, x₂. 51. OB. There are five slack variables named x₁, x₂, S₁, S₂. 8. OC. There are two slack variables named $₁, $₂. OD. There are three slack variables named 5₁, B₂, B3 Assume the first equation using a slack variable is 4x₁-x₂ +5₁ = 183. What is the second equation after the slack variable is introduced? A. 13x₁ +6x₂ +5=247 OB. 13x₁ +6x₂ +81 +₂=247 OC. 13x, +6x2 +52 = 247 What is the third equation after the slack variable is introduced? OA 12x₁ + x₂ +5 = 318 OB. 12x₁+x₂2*318 OC. 12x₁ + x₂ +₁ +₂=318 Maximize: z=10x₁ +3x₂ subject to: with 4x₁-x2 183 13x, +6x2 < 247 12x +%₂318 x₁20, X₂20arrow_forwardPetrolemarrow_forwardThe area of a triangle with sides of length a, b, and c is s(s - a)(s – b)(s - c), where s is half the perimeter of the triangle. We have 60 feet of fence and want to fence a triangular-shaped area. Part A: Formulate the problem as a constrained nonlinear program that will enable us to maximize the area of the fenced area, with constraints. Clearly indicate the variables, objective function, and constraints. Hint: The length of a side of a triangle must be less than or equal to the sum of the lengths of the other two sides. Part B: Solve the Program (provide exact values for all variables and the optimal objective function).arrow_forwardSubject: Math Topic: Linear Programming Instruction: Use a Table for the Data given, Construct the Objective and Constraints Functions, and find the Solution set and Maximize the Sales, and at the end create a graph 1. A Computer Hardware Company produces 2 kinds of CPU Processors : Processor A and Processor B. It takes 2 hours with a cost of P 1500 to manufacture Processor A , while it takes 3 hours with a cost of P 2800 to manufacture Processor B. The Company’s machine can only Operate 345 hours per month and the Company’s Monthly Production Costs Limit is P 300,000 only. Processor A can be sold for P 4500 and Processor B can be sold at P 6500. What is the number of Processor A and Processor B the Company must produce to maximize sales?arrow_forwardConstraints are in the statement and chartsarrow_forwardLP Model Formulation Please make sure that your answers in LP Model Formulation are composed of Decision Variables, Objective Function and Constraints. 2. Kraft Company wanted to introduce a new version of Tang. The company will make four types of juice, using lychee, strawberry and mango. There are 200 Kilograms of lychee, 300 Kilograms of strawberry and 400 Kilograms of mango. Kraft wants the ratio of the number of containers of mango juice to the number of containers of lychee juice to be at least 8 to 5. They also wanted strawberry juice to be used for no more than 30 percent of the number of containers produced. Also, they want lychee juice to not exceed one-third of the total product. Formulate an LP model that will determine the number of containers of each product to produce in 1 day to maximize the company's profit. The table below shows the price and the cost per container of juice as well as the kilograms of fruits required to produce one container of juice. Product Mango…arrow_forwardAn ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below. Medium Cost per Ad # Reached Exposure Quality TV 500 10,000 30 Radio 200 3000 40 Newspaper 400 5000 25 Let T = number of TV ads; R = number of radio ads; and N = number of newspaper ads. The constraint representing the exposure quality of Radio ads must be at least twice those of TV and Newspaper ads is:arrow_forward1. Maximization Model. Answer in complete solution.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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