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Scenario:

A furniture manufacturer makes two kinds of desks: Standard and Executive. These desks are then sold at Rs 300 for the Standard type and Rs 330 for the Executive type to office furniture wholesaler; there is an unlimited market for any mix of these desks, at least in the manufacturer’s production capacity. Each desk has to go through four basic operations: cutting of timber, joining of the pieces, pre-finishing and final finish. Each unit of the Standard desk produced takes 48 minutes of cutting time, 2 hours of joining, and 40 minutes of pre-finishing and 4 hours of final finishing time. Each unit of the Executive desk required 72 minutes of cutting, 3 hours of joining, 2 hours of pre-finishing and 5 hours and 20 minutes of final finishing time. The daily capability for each operation amounts to 16 hours of cutting, 30 hours of joining, 16 hours of pre-finishing and 64 hours of final finishing time. It costs the furniture manufacturer Rs 260 and Rs 280 to make one unit of Standard desk and one unit of Executive desk respectively.
 
problem 1: Devise the linear programming model for this problem.

problem 2: Plot a graph labelling and indicating clearly all the constraints, the feasible region (R) and the optimal point (X).

problem 3: Analyze the product mix that will maximise the total revenue using the corner point method.

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