Question

# MGT 5180 Homework #3

Professor Ben Asslani

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__Homework #3: Non-Linear & Goal Programming__

(1). ** From Chapter 4, Problem 5**:

*pages 152 - 154*

An appliance warehouse stocks the following items: microwaves, ranges, washers, dryers, and dishwashers. Operational data in the *ch4_P5appliances *file located in the companion website indicate the demand for each appliance during the last 12 months. The following table stores additional operational data for each appliance:

You are the logistics manager and would like to calculate the each item category to minimize overall inventory cost. The Economic Order Quantity model can be used to optimally calculate the amount of inventory for each item group with the goal of minimizing the storage (holding) cost and ordering cost. However, there are some constraints such as storage capacity (5,000 cubic feet) and purchasing budget $2.0 million) which may make the optimal solution of EOQ model not feasible.

1. Find a solution for the above problem as a linear programming model.

a. What is the optimal order inventory level for each appliance?

Are these quantities different form the values calculated via the EOQ formula?

Why?

b. What is the value of the objective function (holding plus ordering cost) for the above solution?

2. The company will implement a quantity discount policy when pricing each appliance.

The following table represents the price for each appliance when the warehouse orders a specified quantity range.

For example, if the warehouse orders up to 40 microwaves, then the price is $160, when the ware house orders from 41-60 microwaves the price drops to $150, and so on.

1. Adjust the Excel template to reflect the price discount using vlookup functions.

2. Can you find a formula and solution the problem with an NLP model to determine the optimal order quantity which maximizes the total profit.

Note that the profit for each appliance can be calculated as:

*((selling price - discounted purchasing price)*(monthly demand)) - total cost per month.*

*3. *Find Analysis the Answer Report to identify the final values for the decision variables, binding and not binding constraints, and the impact of changing the right hand side values of the constraints in the final value of the objective function*.
*

(2) ** From Chapter 5, Problem 6**:

*Pages 186-188*

A shoe manufacturer would like to determine the best way to maximize profits on three new shoe models. The new models belong in the following categories: running, hiking, and casual. The model in the *running *category will result in a profit of $30 per item, the model in the *hiking *category will result in $40 profit per item, and the model in the casual category will
result in $20 per item. The manufacturer has limitations in terms of production hours to consider: 1000 hours of production time available per month in the cutting/sewing department, 600 hours per month in the finishing department, and only 500 hours per month available in the packaging/shipping department. The following table illustrates the production time requirements for each shoe model.

The production manager is seeking to optimize production according to several company goals.

(P1 = 500) Priority 1: The manufacturer should produce at least 100 pair of shoes for each model.

(P2 = 400) Priority 2: The manufacturer should meet monthly demand of 300 pair per month for running shoes and casual shoes.

(P3 = 100) Priority 3: The manufacturer should utilize the available machine hours.

1. Find an adequate solution the problem as a simple LP

2. can you Define deviational variables for goal programming model

3. What is GP and system constraints

4. what is / can you find a GP model

5. what is a solution the problem with Solver and what is the result of the analysis

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