Problem:
Linear Programming - Bikes and Furniture
1. A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult open trail, the adult cityscape, the girl's sea sprite, and the boy's trail blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The linear program model should maximize profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. The adult bikes need two feet, but each children's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The children's bike need 4 hours each; the open trail needs 5 hours and the cityscape needs 6 hours. The store would like to place an order for at least 275 bikes.
How many of each kind of bike should be ordered and what will the profit be?
Formulate a model for this problem.
2. A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq ft and each chair utilizes 30 sq ft. At least five sofas and at least five chairs are to be displayed.
Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model the following objective:
Maximize the total expected daily profit. The following choices are given:
a. Max s + c
b. Max .03s + 05c
c. Max 6s + 5c