Explanation Given: The order placed by United Delivery Service for at least 300 quarter-ton, 450 half-ton, and 450 three-quarter-ton panel trucks. The Detroit plant of U.S. Motors produces 30 quarter-ton trucks, 60 half-ton trucks, and 90 three-quarter-ton trucks each week, at the total cost of $540, 000 and The Los Angeles plant of U.S. Motors produces 60 quarter ton trucks, 45 half-ton trucks, and 30 three-quarter-ton trucks each week, at a total cost of $360, 000 . Approach: 1. List the independent variables. 2. List the constraints and translate them into linear inequalities. 3. Find the objective and translate it into a function. 4. Graph the region of possible solutions. 5. Find all corner points and the z-values associated with these points. 6. Find maximum/minimum. Calculation: Consider x weeks of production in Detroit and y weeks production in Los Angeles. So x ≥ 0 and y ≥ 0 . We make the following table from the given data: Types of trucks Detroit ( x ) Los Angeles ( y ) Demand Quarter-ton 30 60 300 Half-ton 60 45 450 Three-Quarter-ton 90 30 450 Cost $540, 000 $360, 000 Since, the order placed by United Delivery Service for at least 300 quarter-ton, 450 half-ton, and 450 three-quarter-ton panel trucks, we have constraints: 30 x + 60 y ≥ 300 60 x + 45 y ≥ 450 90 x + 30 y ≥ 450 Total cost Z on x weeks production in Detroit and y weeks production in Los Angeles is Z = 540 , 000 x + 360 , 000 y So, the mathematical formulation of the problem is: Minimize Z = 540 , 000 x + 360 , 000 y subject to the constraints: 30 x + 60 y ≥ 300 60 x + 45 y ≥ 450 90 x + 30 y ≥ 450 x ≥ 0 and y ≥ 0 Let us graph the feasible region of the above system of inequalities. The feasible region (shaded) is unbounded.

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 12.1, Problem 23E

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Number of weeks of production in Detroit and in Los Angeles for a minimum cost and the minimum cost

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Ch. 12.0 - In Exercises 1-8, graph the region of the...Ch. 12.0 - Prob. 2E Ch. 12.0 - Prob. 3E Ch. 12.0 - In Exercises 1-8, graph the region of the...Ch. 12.0 - Prob. 5E Ch. 12.0 - Prob. 6E Ch. 12.0 - In Exercises 1-8, graph the region of the...Ch. 12.0 - Prob. 8E Ch. 12.0 - Prob. 9E Ch. 12.0 - Prob. 10E

Ch. 12.0 - Prob. 11E Ch. 12.0 - Prob. 12E Ch. 12.0 - Prob. 13E Ch. 12.0 - Prob. 14E Ch. 12.0 - Prob. 15E Ch. 12.0 - Prob. 16E Ch. 12.0 - Prob. 17E Ch. 12.0 - Prob. 18E Ch. 12.0 - Prob. 19E Ch. 12.0 - Prob. 20E Ch. 12.0 - Prob. 21E Ch. 12.0 - Prob. 22E Ch. 12.0 - Prob. 23E Ch. 12.0 - Prob. 24E Ch. 12.0 - Prob. 25E Ch. 12.0 - Prob. 26E Ch. 12.0 - Prob. 27E Ch. 12.0 - Prob. 28E Ch. 12.0 - Prob. 29E Ch. 12.0 - Prob. 30E Ch. 12.0 - Prob. 31E Ch. 12.0 - Prob. 32E Ch. 12.0 - Prob. 33E Ch. 12.0 - Prob. 34E Ch. 12.0 - Prob. 35E Ch. 12.0 - Prob. 36E Ch. 12.0 - Prob. 37E Ch. 12.0 - Prob. 38E Ch. 12.0 - Prob. 39E Ch. 12.0 - Prob. 40E Ch. 12.0 - Prob. 41E Ch. 12.0 - Prob. 42E Ch. 12.0 - Prob. 43E Ch. 12.0 - Prob. 44E Ch. 12.0 - Prob. 45E Ch. 12.0 - Prob. 46E Ch. 12.0 - In Exercises 3749. use a graphing calculator to...Ch. 12.0 - Prob. 48E Ch. 12.0 - Prob. 49E Ch. 12.1 - In Exercises 1-6, convert the information into a...Ch. 12.1 - Prob. 2E Ch. 12.1 - In Exercises 1-6, convert the information into a...Ch. 12.1 - Prob. 4E Ch. 12.1 - In Exercises 1-6, convert the information into a...Ch. 12.1 - Prob. 6E Ch. 12.1 - In Exercises 7-16, use the method of linear...Ch. 12.1 - In Exercises 7-16, use the method of linear...Ch. 12.1 - In Exercises 7-16, use the method of linear...Ch. 12.1 - In Exercises 7-16, use the method of linear...Ch. 12.1 - Prob. 11E Ch. 12.1 - Notel Chips manufactures computer chips. Its two...Ch. 12.1 - Global Air Lines has contracted with a tour group...Ch. 12.1 - Compucraft sells personal computers and printers...Ch. 12.1 - The Appliance Barn has 2,400 cubic feet of storage...Ch. 12.1 - City Electronics Distributors handles two lines of...Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - How much of her available time would be unused if...Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - In Exercises 21-24, the region of possible...Ch. 12.1 - Prob. 23E Ch. 12.1 - In Exercises 21-24, the region of possible...Ch. 12.1 - Prob. 25E Ch. 12.1 - Is it possible for an unbounded region to have...Ch. 12.1 - Prob. 27E Ch. 12.1 - In Example 2, Petes Coffees mixes Colombian beans...Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - What was surprising about the awarding of a Nobel...Ch. 12.1 - Prob. 37E Ch. 12.1 - Answer the following questions using complete...Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.CR - Prob. 1CR Ch. 12.CR - Prob. 2CR Ch. 12.CR - Prob. 3CR Ch. 12.CR - Prob. 4CR Ch. 12.CR - Prob. 5CR Ch. 12.CR - Prob. 6CR Ch. 12.CR - Prob. 7CR Ch. 12.CR - Prob. 8CR Ch. 12.CR - Prob. 9CR Ch. 12.CR - Prob. 10CR Ch. 12.CR - Prob. 11CR Ch. 12.CR - Prob. 12CR Ch. 12.CR - Prob. 13CR Ch. 12.CR - In Exercises 11-17, solve the given linear...Ch. 12.CR - The Mowson Audio Co. makes stereo speaker...Ch. 12.CR - The Stereo Guys store sells two lines of personal...Ch. 12.CR - Prob. 17CR Ch. 12.CR - Prob. 18CR Ch. 12.CR - Answer the following questions using your own...

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Number of weeks of production in Detroit and in Los Angeles for a minimum cost and the minimum cost

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Number of weeks of production in Detroit and in Los Angeles for a minimum cost and the minimum cost