§Chandler Enterprises produces two competing products: A and B, The company wants to sell these products to two groups of customers: group 1 and group 2. The value each customer places on a unit of A and B is as shown in Table 56. Each customer will buy either product A or product B, but not both. A customer is willing to buy product A if she believes that
Value of product A – price of product A
≥ Value of product B – price of product B
and
Value of product A – price of product A ≥ 0
A customer is willing to buy product B if she believes that Value of product B – price of product B
≥ value of product A – price of product A
and
Value of product B – price of product B ≥ 0
Group 1 has 1,000 members, and group 2 has 1,500 members. Chandler wants to set prices for each product that ensure that group 1 members purchase product A and group 2 members purchase product B Formulate an LP that will help Chandler maximize revenues.
table 56
| Group 1 Customer | Group 2 Customer |
Value of A to | $10 | $12 |
Value of B to | $8 | $15 |
§Based on Dobson and Kalish (1988).
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