In Exercises 1–6, determine the dual problem of the given linear programming problem.
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Finite Mathematics & Its Applications (12th Edition)
- 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_forwardSolve the following linear programming model graphically.arrow_forwardformulate this problem as a linear programming modelarrow_forward
- Define and discuss the linear programming technique?arrow_forwardAn economy produces steel and lumber. To produce 1 ton of steel requires the consumption of .5 tons of steel and 2 tons of lumber (that's 2 whole tons, not 0.2 tons). To produce 1 ton of lumber requires the consumption of .2 tons of steel, and 0 tons of lumber. Suppose there is a demand for 3 tons of steel and 1 ton of lumber. If a production schedule is calculated to meet this demand, how many tons of steel are produced? Group of answer choicesarrow_forwardAn economy produces steel and lumber. To produce 1 ton of steel requires the consumption of .5 tons of steel and 2 tons of lumber (that's 2 whole tons, not 0.2 tons). To produce 1 ton of lumber requires the consumption of .2 tons of steel, and 0 tons of lumber. Suppose there is a demand for 3 tons of steel and 1 ton of lumber. If a production schedule is calculated to meet this demand, how many tons of steel are produced?arrow_forward
- You are given the ILP model below: Мaximize Z = -3x1 + 5x2, subject to 5x1 – 7x2 > 3 and X; < 3 X; 2 0 X; is integer, for j = 1, 2. Convert the ILP model above into a BIP model. TIP: You will need to perform the necessary analysis on the constraints to determine the maximum value, u.arrow_forwardSolve the following linear programming graphically [8]Minimize and maximize: z = 3x + 9ySubject to the constraints:x + 3y ≥ 6x + y ≤ 10x ≤ yx ≥ 0; y ≥ 0arrow_forwardAn experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 600 minutes. The white mice must spend 10 minutes in environment I and 25 minutes in environment II, and the rabbits must spend 12 minutes in environment I and 15 minutes in environment II. Find the maximum possible number of animals that can be used in the experiment and find the number of white mice and the number of rabbits that can be used. number of animals = ?number of white mice = ?number of rabbits = ?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning