🗊Презентация Optimization. Maximizing profit, minimizing cost

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Слайды и текст этой презентации


Слайд 1





7.6-Optimization
Описание слайда:
7.6-Optimization

Слайд 2





Example 1
A grocer sells 50 loaves of bread a day. The cost is $0.65 a loaf. The grocer estimates that for each $0.05 price increase, 2 fewer loaves of bread will be sold.
How much should one loaf of bread cost to maximize the income?
What is the maximum income he will make?
Описание слайда:
Example 1 A grocer sells 50 loaves of bread a day. The cost is $0.65 a loaf. The grocer estimates that for each $0.05 price increase, 2 fewer loaves of bread will be sold. How much should one loaf of bread cost to maximize the income? What is the maximum income he will make?

Слайд 3





What are we finding?
The price of the loaf of bread which maximizes the profit for the grocer.  
The total amount of income the grocer will make at the price from part a.
Описание слайда:
What are we finding? The price of the loaf of bread which maximizes the profit for the grocer. The total amount of income the grocer will make at the price from part a.

Слайд 4





What two equations can we write?
We know information about the:
Описание слайда:
What two equations can we write? We know information about the:

Слайд 5





The two equations
Let .
How much is a single loaf of bread after  increases?
How many loafs of bread will be sold after  increases?
Описание слайда:
The two equations Let . How much is a single loaf of bread after increases? How many loafs of bread will be sold after increases?

Слайд 6





Writing a equation for Income
Simplify…
Описание слайда:
Writing a equation for Income Simplify…

Слайд 7





Take the derivative and set to 
 This means that in order to maximize the income the price should be increased 6 times.
Описание слайда:
Take the derivative and set to This means that in order to maximize the income the price should be increased 6 times.

Слайд 8





Back to the questions
How much should one loaf of bread cost to maximize the income?
What is the maximum income he will make?
Описание слайда:
Back to the questions How much should one loaf of bread cost to maximize the income? What is the maximum income he will make?



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