Fertilizer supply is explained by the following equation: ?? = 3,000? where ?? is the supply per year and ? is the price of fertilizer per ton. Demand for fertilizer is explained by: ?? = 500,000 - 20,000? where tons there is a lot of fertilizer demanded every year. The marginal external cost of $ 30 is associated with the production per ton of fertilizer due to pollution associated with fertilizer production. Answer the following questions and explain your answer by showing your work.Competitive market price is $21.74. How many tons of fertilizer will be produced per year at that price?

Fertilizer supply is explained by the following equation: ?? = 3,000? where ?? is the supply per year and ? is the price of fertilizer per ton. Demand for fertilizer is explained by: ?? = 500,000 - 20,000? where tons there is a lot of fertilizer demanded every year. The marginal external cost of $ 30 is associated with the production per ton of fertilizer due to pollution associated with fertilizer production. Answer the following questions and explain your answer by showing your work.Competitive market price is $21.74. How many tons of fertilizer will be produced per year at that price?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 56P

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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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