5. Changes in the right-hand side. JOBCO produces two products on two machines. A unit of...

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5. Changes in the right-hand side. JOBCO produces two products on two machines. A unit of Product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For Product 2, a unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues per unit of products 1 and 2 are $30 and $20, respectively. The total daily processing time available for each machine is 8 hours. Letting X and X2 represent the daily number of units of products 1 and 2, respectively, the LP model is given as max z = 30x1 + 20x2 s.t. 2X1 + X2 8 X1 + 3x 8 X, X 0 (a) What happens if the daily capacity of machine 1 increases to 9? (b) If JOBCO can increase the capacity of both machines, which machine should receive higher priority? (c) A suggestion is made to increase the capacities of machines 1 and 2 at the additional cost of $10/hr. Is this advisable? (d) If the capacity of machine 1 is increased from the present 8 hours to 13 hours, how will this increase impact the optimum revenue? (e) Suppose that the capacity of machine 1 is increased to 20 hrs, how will this increase impact the optimum revenue? (f) We know that the change in the optimum objective value equals (dual price change in resource) so long as the change in the resource is within the feasibility range. What about the associated optimum values of the variables? 5. Changes in the right-hand side. JOBCO produces two products on two machines. A unit of Product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For Product 2, a unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues per unit of products 1 and 2 are $30 and $20, respectively. The total daily processing time available for each machine is 8 hours. Letting X and X2 represent the daily number of units of products 1 and 2, respectively, the LP model is given as max z = 30x1 + 20x2 s.t. 2X1 + X2 8 X1 + 3x 8 X, X 0 (a) What happens if the daily capacity of machine 1 increases to 9? (b) If JOBCO can increase the capacity of both machines, which machine should receive higher priority? (c) A suggestion is made to increase the capacities of machines 1 and 2 at the additional cost of $10/hr. Is this advisable? (d) If the capacity of machine 1 is increased from the present 8 hours to 13 hours, how will this increase impact the optimum revenue? (e) Suppose that the capacity of machine 1 is increased to 20 hrs, how will this increase impact the optimum revenue? (f) We know that the change in the optimum objective value equals (dual price change in resource) so long as the change in the resource is within the feasibility range. What about the associated optimum values of the variables?