In Exercises 25–32, find the optimal value for the linear programming problem.
Maximize the objective function
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Chapter 3 Solutions
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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_forwardUse your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.arrow_forwardFormulate the dual of the linear program givenarrow_forward
- The following diagram represents various flows that can occur through a sewage treatment plant with the numbers on arcs representing the maximum flow (in tonnes of sewage per hour) that can be accommodated. The plant manager wants to know the system's capacity. 12 1 2 8 9 15 3 16 6 7 5 4 12 Formulate the algebraic model for this problem by writing down the decision variables, objective function, and constraints.arrow_forwardIn Exercises 5-8, explain why the linear programming problem is not in standard form as given. 5. (Minimize) Objective function: z = x₁ + x₂ Constraints: x₁ + 2x₂ = 4 X1, X₂ ≥ 0arrow_forwardNeed only a handwritten solution only (not a typed one).arrow_forward
- Answer the last 3 parts d, e, farrow_forwardLPParrow_forwardAt least 800 kg of specially produced feed is used in a farm per day. This special productionforage; obtained from a mixture of corn and soy flour in accordance with the following composition ratiosare being. The composition of this special production feed must contain at least 30% protein and at most 5% fiber.has.a. Linear programming (DP) model that gives the minimum cost daily feed mixinstall. In the model you have established, "Determining the decision variable", "Objective FunctionYou must clearly state the steps of "Defining" and "Expressing constraints".b. Using the Graphic Method, show the possible solution area and show the best possible solution of the LP model.Determine the solution.arrow_forward
- a)Would profit be maximized if the objective function y=50x_+40xm+20x, was assumed (under the same contraints) for the same problem? Mr. Omar-doh sells sheep during the annual county auction. He wishes to use linear programming to describe his problem and therefore consults the UoN for assistance. Sheep come in three sizes: large, medium, and small. The large sheep (x.) cost Kshs. 3,500 and sell for Kshs.6,000 each; the medium sheep (x.) cost Kshs.3,000 and sell for Kshs.5,000 each; the small sheep (x) cost Kshs. 1,500 and sell for Kshs.2,500 each. Omar-doh must order at least twenty sheep of each type. He can spend no more than Kshs.0.3 million on sheep investment. His space limitations are such that he cannot exceed 60 units of the large and medium sheep combined. He wants to obtain a gross revenue of at least half a million from selling sheep. He further wants to maximize his profits subject to all the constraints above.arrow_forwardI need help developing a linear programming model to minimize the total dollars needed to be invested now to meet the expansion cash needs in the next 8 years. Your corporation has just approved an 8-year expansion plan to grow its market share. The plan requires an influx of cash in each of the 8 years. Management wants to develop a financial plan to ensure the cash needed for the expansion will be available at the beginning of each of the 8 years. The corporation has the following investment options: Security Price per unit Return Rate (%) Years to Maturity 1 $1,200 10.255 5 2 $1,000 6.7550 6 3 $1,175 12.110 7 Savings Account 5.500 Each unit of security 1, 2, and 3 guarantees to pay $1,000 at maturity. Investments in these securities must take place only at the beginning of year 1 and will be held until maturity. Any funds not invested in securities will be invested in a savings account that pays the annual interest rates…arrow_forward4. The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand according to the following linear equation. v = 400 – 1.2p REQUIREMENT: Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.arrow_forward
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