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A company produces widgets at plants 1 and 2. It costs 135 x 1/2 dollars to produce x units at plant 1 and 260 x 1/3 dollars to produce x units at plant 2. Each plant can produce up to 1000 units. Each unit produced can be sold for $12. At most 1700 widget can be sold. Determine how the company can maximize its profit.

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

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Chapter
Section
BuyFindarrow_forward

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 7, Problem 48P
Textbook Problem
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A company produces widgets at plants 1 and 2. It costs 135x1/2 dollars to produce x units at plant 1 and 260x1/3 dollars to produce x units at plant 2. Each plant can produce up to 1000 units. Each unit produced can be sold for $12. At most 1700 widget can be sold. Determine how the company can maximize its profit.

Summary Introduction

To determine: The way the company can maximize the profit.

Non-linear programming (NLP):

Non-linear programming (NLP) is used in complex optimization problems where the objectives or constraints or sometimes both are non-linear functions of the decision variables. A model can be termed as non-linear for more than one reason.

Explanation of Solution

Model:

Formula:

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Chapter 7 Solutions

Practical Management Science
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Ch. 7.3 - ELECTRICITY PRICING AT FLORIDA POWER AND LIGHT...Ch. 7.3 - In the electricity pricing model in Example 7.4,...Ch. 7.3 - Continuing Problem 6, suppose the company is...Ch. 7.3 - PRICING SUITS AT SULLIVANS Sullivans is a retailer...Ch. 7.3 - Continuing the previous problem (the model in part...Ch. 7.4 - In estimating the advertising response function in...Ch. 7.4 - The best-fitting advertising response function in...Ch. 7.4 - In judging the fit of the estimated response...Ch. 7.4 - Starting with the solution to the advertising...Ch. 7.4 - The preceding problem indicates how fewer...Ch. 7.4 - In the solution to the advertising selection model...Ch. 7.4 - The advertising response function in Equation...Ch. 7.4 - In Example 7.5, we implied that each of the five...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.6 - The file P07_28.xlsx lists the scores of all NFL...Ch. 7.6 - Carry out the suggestion in Modeling Issue 3. That...Ch. 7.6 - Carry out the suggestion in Modeling Issue 2 for...Ch. 7.6 - The file P07_31.xlsx contains scores on all of the...Ch. 7.6 - By the time you are reading this, the 2016 NFL...Ch. 7.6 - By the time you are reading this, the 20162017 NBA...Ch. 7.6 - The method for rating teams in Example 7.8 is...Ch. 7.7 - For each of the following, answer whether it makes...Ch. 7.7 - Add a new stock, stock 4, to the model in Example...Ch. 7.7 - In the model in Example 7.9, stock 2 is not in the...Ch. 7.7 - The stocks in Example 7.9 are all positively...Ch. 7.7 - The file P07_39.xlsx contains historical monthly...Ch. 7.7 - This problem continues using the data from the...Ch. 7.7 - Continuing the previous problem, find the...Ch. 7.7 - In many cases, the portfolio return is at least...Ch. 7.8 - Given the data in the file Stock Beta.xlsx,...Ch. 7.8 - Solve the previous problem, but analyze GE instead...Ch. 7 - Suppose Ford currently sells 250,000 Ford Mustangs...Ch. 7 - Suppose the current exchange rate is 115 yen per...Ch. 7 - Another way to derive a demand function is to...Ch. 7 - A company produces widgets at plants 1 and 2. It...Ch. 7 - If a monopolist produces q units, she can charge...Ch. 7 - It costs a company 15 to purchase an hour of labor...Ch. 7 - In the previous problem, what is the minimum-cost...Ch. 7 - The cost per day of running a hospital is 300,000...Ch. 7 - Two companies are producing widgets. It costs the...Ch. 7 - A company manufactures two products. If it charges...Ch. 7 - A brewing company has 100,000 to spend on...Ch. 7 - QH Company advertises during soap operas and...Ch. 7 - A beer company has divided Bloomington into two...Ch. 7 - A company uses raw material to produce two...Ch. 7 - JJ has given you 12 million to spend on...Ch. 7 - Based on Kolesar and Blum (1973). Suppose that a...Ch. 7 - A company has five factories. The x- and...Ch. 7 - Monroe County is trying to determine where to...Ch. 7 - Consider three investments. You are given the...Ch. 7 - You have 50,000 to invest in three stocks. Let Ri...Ch. 7 - An oil company must determine how many barrels of...Ch. 7 - Suppose that you are hiring a weather forecaster...Ch. 7 - The cost of producing x units of a product during...Ch. 7 - Four items are for sale in the Dollar Value store....Ch. 7 - Most economies have a goal of maximizing the...Ch. 7 - Each morning during rush hour, 10,000 people want...Ch. 7 - Based on Grossman and Hart (1983). A salesperson...Ch. 7 - Find the minimum perimeter rectangle having area...Ch. 7 - You are given that the two nonhypotenuse sides of...Ch. 7 - A cylindrical soda can has a volume of 20 cubic...Ch. 7 - City B is 10 miles downstream from city A. City A...Ch. 7 - You can swim two miles per hour and run six miles...Ch. 7 - A triangle has a 5-inch side and a 12-inch side....Ch. 7 - Your company is about to market a new golf club....Ch. 7 - For the product mix examples (Examples 3.1 and 3.2...Ch. 7 - For the oil blending example (Example 4.4 in...Ch. 7 - For the aggregate planning example (Example 4.3 in...Ch. 7 - Consider the sports ratings model in section 7.6....Ch. 7 - Consider the sports ratings model in section 7.6....Ch. 7 - UE is going to invest 400 million to acquire...Ch. 7 - Your family owns a large farm that can grow wheat,...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...

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