Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables) b. Solve your model with Excel Solver. c. How many of each kind of bike should be ordered and what will the profit be?
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A large sporting goods store is placing an order for bicycles with its supplier. Four types of 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:
- The first constraint is about 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.
- The second constraint is about availability of assembly time. 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.
- As the third constraint, the store would like to place an order for at least 275 bikes.
a. Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables)
b. Solve your model with Excel Solver.
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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- Doc Nix Productions sells specialty T-Shirts that are sold at a single basketball game each. Doc Nix is trying to decide how many to buy for an upcoming game. During the game itself, which lasts one evening, Doc can sell T-Shirts for $10 apiece. However, when the game ends unsold T-shirts have no value. Due to a licensing agreement, Doc needs to make sure that leftover shirts are destroyed using a method that ends up costing $0.50 for each unsold T-Shirt. It costs Doc $6.50 to buy a specialty T-Shirt from the supplier. The supplier he uses has a cost per shirt of $2. Doc estimates that demand is distributed as shown below. Demand 300 350 400 450 500 550 Probability 0.05 0.15 0.20 0.10 0.30 0.20 How many specialty T-Shirts should Doc Nix buy from the supplier to maximize his profits? What is his expected profit? What is the total supply chain profit?Birka Styles & Co is introducing a new line of beachwear for their retail stores. The manager needs to decide how many lots of the new beachwear to order for their stores. The marketing came up with a payoff table (see below) considering information about the price, projected sales level, and cost of inventory and ordering. DEMAND Order size Low Medium High 1 lot 12,000 15,000 15,000 2 lots 9,000 25,000 35,000 3 lots 6,000 35,000 60,000 The owner wants to use the Hurwicz method and gave the manager a Hurwica alpha (α) of 0.6. How many lots should the manager order?6-20 Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost? a- EOQ=2×A×OC where A is Annual demand O is ordering cost C is Carrying Cost EOQ=2×100,000×100.005=400,000,000=20,000 How many orders per year would be placed? What would the annual ordering cost be? b- Number of Orders=Annual Demand EOQ=100,000 20,000=5 orders Ordering Cost=Number of Orders×Ordering Cost =5×10=$50 What would the average inventory be? What would the annual holding…
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