30. Didierlimited manufactures three products; tables, sideboards and chairs which require special material, timber and labour. In a given week, there are 92 units of special material, 116 pieces of timber and 140 hours of labour. The requirements of special materials are 2 units, 4 units and 2 units , for a + sideboard and chair respectively Manufacturing a table or a sideboard requires 2 hours of labou while a chair requires 4 hours. Timber requirements are 4 pieces, 2 pieces and 2 pieces for a tai sideboard and a chair respectively. At least 2 tables and 4 chairs must be made. The profit contributions are ￡30,￡40,￡20 for a table, sideboard and chair respectively. Formulate the underlying LP and solve it to advice Didier limited how to maximize profits.

Question

30. Didierlimited manufactures three products; tables, sideboards and chairs which require special material, timber and labour. In a given week, there are 92 units of special material, 116 pieces of timber and 140 hours of labour. The requirements of special materials are 2 units, 4 units and 2 units , for a + sideboard and chair respectively Manufacturing a table or a sideboard requires 2 hours of labou while a chair requires 4 hours. Timber requirements are 4 pieces, 2 pieces and 2 pieces for a tai sideboard and a chair respectively. At least 2 tables and 4 chairs must be made. The profit contributions are ￡30,￡40,￡20 for a table, sideboard and chair respectively. Formulate the underlying LP and solve it to advice Didier limited how to maximize profits.

Answer 1

Let x, y, and z represent the number of tables, sideboards, and chairs manufactured respectively. The objective function to maximize is the total profit, which is given by:Profit = 30x + 40y + 20zSubject to the following constraints:1. Special material constraint: 2x + 4y + 2z ≤ 922. Timber constraint: 4x + 2y + 2z ≤ 1163. Labour constraint: 2x + 2y + 4z ≤ 1404. Minimum production constraint: x ≥ 2, y ≥ 0, z ≥ 4To solve this linear programming problem, we can use the graphical method or the simplex method. In this case, the graphical method is more straightforward.First, plot the feasible region on a graph by plotting the lines representing the constraints. The feasible region is the area where all the constraints are satisfied.Next, plot the objective function line on the graph. The objective function line represents the profit that Didier Limited can make for different combinations of tables, sideboards, and chairs.Finally, find the point where the line intersects the feasible region. This point represents the optimal solution that maximizes the profit for Didier Limited.By solving the linear programming problem, we find that Didier Limited should manufacture 2 tables, 24 sideboards, and 4 chairs to maximize their profit.

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