Sales representatives sell two products A and B. Based on historical data there is an average 20 euro commission for every call on product A and a 10 euro commission for every call on product B. Data also shows that sales representatives spend about 3 hours per call for product A and 2 hour for product B. The company requires at least 25 calls per month for each product and not more than 100 calls per month on any one product. How should the sales representatives allocate their monthly 165 working hours between making calls selling products A and B if they want to maximize their commission? a) Mathematically formulate the LP model for maximizing commissions (=primal problem) b) Mathematically formulate the dual problem of the primal problem. Implement both LP models (primal and dual) using Excel Solver. c) Report the optimal objective functions, decision variable values and the shadow prices of both the primal and dual problems. d) Confirm that these numbers are in line with the properties known to hold between primal and dual problems. Report these results
Sales representatives sell two products A and B. Based on historical data there is an average 20 euro commission for every call on product A and a 10 euro commission for every call on product B. Data also shows that sales representatives spend about 3 hours per call for product A and 2 hour for product B. The company requires at least 25 calls per month for each product and not more than 100 calls per month on any one product. How should the sales representatives allocate their monthly 165 working hours between making calls selling products A and B if they want to maximize their commission?
a) Mathematically formulate the LP model for maximizing commissions (=primal problem)
b) Mathematically formulate the dual problem of the primal problem.
Implement both LP models (primal and dual) using Excel Solver.
c) Report the optimal objective functions, decision variable values and the shadow prices of both the primal and dual problems.
d) Confirm that these numbers are in line with the properties known to hold between primal and dual problems. Report these results
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