Products A, B and C are sold door to door. Product A costs Birr 3 per unit to make, takes 10 minutes to sell and costs Birr 0.50 to deliver to customers. B costs Birr 5 per unit to make, takes 15 minutes to sell, and is left with the customer at the time of sale. C costs Birr 4, takes 12 minutes to sell and costs Birr 1 to deliver. During any given week, a sales man is allowed to draw up to Birr 500 worth of A, B and C at a cost and delivery expenses not exceeding Birr 75. if a salesman’s selling time is not expected to exceed 30 hours in a week, and the salesman’s profit (net after all expenses) is Birr 1 each on a unit of A and B, and Birr 2 on a unit of C; what combination of sales of A, B and C will lead to maximum profit.
Required:
A. Formulate both the primal and the dual linear programming model for the problem
B. Solve the dual model using simplex algorithm
C. Derive the primal optimal solution from the dual optimal solution
Answers
Answer:
c
Explanation:
Products A, B and C are sold door to door. Product A costs Birr 3 per unit to make, takes 10 minutes to sell and costs Birr 0.50 to deliver to customers. B costs Birr 5 per unit to make, takes 15 minutes to sell, and is left with the customer at the time of sale. C costs Birr 4, takes 12 minutes to sell and costs Birr 1 to deliver. During any given week, a sales man is allowed to draw up to Birr 500 worth of A, B and C at a cost and delivery expenses not exceeding Birr 75. if a salesman’s selling time is not expected to exceed 30 hours in a week, and the salesman’s profit (net after all expenses) is Birr 1 each on a unit of A and B, and Birr 2 on a unit of C; what combination of sales of A, B and C will lead to maximum profit.
Required:
A. Formulate both the primal and the dual linear programming model for the problem
B. Solve the dual model using simplex algorithm
C. Derive the primal optimal solution from the dual optimal solution
Explanation:
Products A, B and C are sold door to door. Product A costs Birr 3 per unit to make, takes 10 minutes to sell and costs Birr 0.50 to deliver to customers. B costs Birr 5 per unit to make, takes 15 minutes to sell, and is left with the customer at the time of sale. C costs Birr 4, takes 12 minutes to sell and costs Birr 1 to deliver. During any given week, a sales man is allowed to draw up to Birr 500 worth of A, B and C at a cost and delivery expenses not exceeding Birr 75. if a salesman’s selling time is not expected to exceed 30 hours in a week, and the salesman’s profit (net after all expenses) is Birr 1 each on a unit of A and B, and Birr 2 on a unit of C; what combination of sales of A, B and C will lead to maximum profit.
Required:
A. Formulate both the primal and the dual linear programming model for the problem
B. Solve the dual model using simplex algorithm
C. Derive the primal optimal solution from the dual optimal solution