Toy World (Mauritius) produces two types of toy model trains, the Steamer train and the Lightning train. Three machines are required to produce each type; these machines are classified as X, Y, and Z. Each Steamer train requires 7 minutes of process time on machine X, 4 minutes on machine y, and 10 minutes on machine Z. The lightning train requires 4 minutes on X, 15 minutes on Y, and 16 minutes on Z. Each day there are 420 minutes available on machine X, 600 minutes on machine Y, and 840 minutes on machine Z. The profit for the Steamer train is $8 per unit and that of the Lightning train is $10 per unit. Formulate the complete linear programming model for company’s model trains so as to maximize its profit. Define the decision variables, constraints and objective function clearly. [1] Plot each constraint lines for this linear programming problem on a graph paper. Indicate the feasible region, R clearly on your [1] Solve the linear programming problem to find out the optimal number of Steamer trains and Lightning trains that are required to maximize profit, stating clearly the maximum profit that can be [1] Do any constraints have (nonzero) slack or surplus? If yes, which one(s) and how much slack or surplus does each have? [1] Are any constraints redundant? If yes, which one(s)? Explain [1]

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

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Toy World (Mauritius) produces two types of toy model trains, the Steamer train and the Lightning train. Three machines are required to produce each type; these machines are classified as X, Y, and Z. Each Steamer train requires 7 minutes of process time on machine X, 4 minutes on machine y, and 10 minutes on machine Z. The lightning train requires 4 minutes on X, 15 minutes on Y, and 16 minutes on Z. Each day there are 420 minutes available on machine X, 600 minutes on machine Y, and 840 minutes on machine Z. The profit for the Steamer train is $8 per unit and that of the Lightning train is $10 per unit.

Formulate the complete linear programming model for company’s model trains so as to maximize its profit. Define the decision variables, constraints and objective function clearly. [1]

Plot each constraint lines for this linear programming problem on a graph paper. Indicate the feasible region, R clearly on your [1]

Solve the linear programming problem to find out the optimal number of Steamer trains and Lightning trains that are required to maximize profit, stating clearly the maximum profit that can be [1]

Do any constraints have (nonzero) slack or surplus? If yes, which one(s) and how much slack or surplus does each have? [1]

Are any constraints redundant? If yes, which one(s)? Explain [1]

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