Reference no: EM133153736
Question A:
The Northwest Flower Company owns a greenhouse, which furnishes roses and carnations to florists in Oregon, Washington, and Idaho. The greenhouse can grow any combination of the two flowers. They sell the flowers in "bunches" with 25 blooms to a bunch. They have 10,000 square feet available for planting this year. Each bunch of roses takes about 4 square feet and each bunch of carnations about 5 square feet. Special fertilizer is required for flowers: roses need 5 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 5000 pounds. Sales commitments require the company to grow at least 500 bunches of roses. Profit contributions are $6 per bunch of roses and $8 per bunch of carnations.?
a. Formulate this problem as an LP.
b. Graph this problem.
c. What are the corner points of the feasible region.
d. What is the optimal solution?
QB.
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 LP model should maximize profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; 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.
a. Formulate a model for this problem.
b. Solve your model with any computer package available to you.
c. How many of each kind of bike should be ordered and what will the profit be?
d. What would the profit be if the store had 100 more feet of storage space?
e. If the profit on the Cityscape increases to $35, will any of the Cityscape bikes be ordered?
f. Over what range of assembly hours is the dual price applicable?
g. If we require 5 more bikes in inventory, what will happen to the value of the optimal solution?
h. Which resource should the company work to increase, inventory space or assembly time?
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