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Q4: 3 marks A manufacturer has three machines I, Il and Il installed in his factory. Machines I and Il are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are given in the following table: item Number of hours required on machines III 3. She makes a profit of Rs 600 and Rs 400 on items M andN respectively. How many of each item should she produce so as to maximize her profit assuming that she can sell all the items that she produced? What will be the maximum profit? Hint: the objective function and the constraints for the decision variables for this optimization problem are as follows: Maximize the profit Z= 800x + 200 y Subject to the following constraints: x+2ys12 (constraint on Machine I) (1) 4x +3y 2 36 (constraint on Machine III).. (3) ....... x20, y 20 (non-negative constraint).. -(4) Find the feasible solution for the problem of a decorative item dealer whose LPP is to maximize profit function. (2 Marks) Determine the optimal solution to a LPP occurs at the corners of the feasible region. (1 Mark) 1. 2

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