1. A manufacturer produces two different models: X and Y, of the same products. Model X makes a contribution of Birr 50 per unit and model Y, birr 30 per unit towards total profit. Raw materials R1 and R2 are required for production. At least 18 kg of R1 and 12 of if R2 must be used daily. Also, at most 34 hours of labor are to be utilized. A quantity of 2 kg of R is needed for model X and 1 kg of R for model Y. For each of X and Y, 1 kg of R2 is required. It takes 3 hours to manufacture model X and 2 hours to manufacture model Y. How many units of each model should be produced to maximize the profit? Required: a) Formulate a linear programming model for this problem b) Solve this model graphically and interpret the results c) Analysis the sensitivity of the objective functions and right-hand side values?