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The graph of the profit function in the last problem looks like this: This indicates that the company's profit grows without bound as the quantity of product increases. This is only realistic if the quantity produced is also the quantity sold. In other words, the model only works if the company sells everything it produces. The concept of demand takes into account the fact that in order to sell a certain quantity of product, the price must be adjusted accordingly. A demand function relates the price (dollars per item) to the quantity sold (items). In order to be consistent with our other functions, we will make the quantity sold the independent variable and the price the dependent variable. We will often call the demand function the price function or the price-demand function because of this. Suppose for a company that the price (demand) function is given by p(g) = - 0.3q + 824. 1. If the company chooses to produce 1277 items, what price should it charge in order to sell all of them? dollars per item. If necessary, round to two decimal places. 2. If the company the price to be $297.37 per item, how many can it expect to sell? items. If necessary, round to the nearest whole number. In this scenario, the price is NOT a set price. It varies depending on the quantity. So, unless we know the quantity produced, we cannot write a single number for the price. We write price as an expression involving q. This is given by the demand function. PRICE = - 0.3q + 824 Remember that the revenue function is PRICE times QUANTITY. So, we can find the revenue function by multiplying the demand function by g. 3. Write a formula for the revenue function for this company. R(q) =|

The graph of the profit function in the last problem looks like this: This indicates that the company's profit grows without bound as the quantity of product increases. This is only realistic if the quantity produced is also the quantity sold. In other words, the model only works if the company sells everything it produces. The concept of demand takes into account the fact that in order to sell a certain quantity of product, the price must be adjusted accordingly. A demand function relates the price (dollars per item) to the quantity sold (items). In order to be consistent with our other functions, we will make the quantity sold the independent variable and the price the dependent variable. We will often call the demand function the price function or the price-demand function because of this. Suppose for a company that the price (demand) function is given by p(g) = - 0.3q + 824. 1. If the company chooses to produce 1277 items, what price should it charge in order to sell all of them? dollars per item. If necessary, round to two decimal places. 2. If the company the price to be $297.37 per item, how many can it expect to sell? items. If necessary, round to the nearest whole number. In this scenario, the price is NOT a set price. It varies depending on the quantity. So, unless we know the quantity produced, we cannot write a single number for the price. We write price as an expression involving q. This is given by the demand function. PRICE = - 0.3q + 824 Remember that the revenue function is PRICE times QUANTITY. So, we can find the revenue function by multiplying the demand function by g. 3. Write a formula for the revenue function for this company. R(q) =|

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...
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The graph of the profit function in the last problem looks like this: This indicates that the company's profit grows without bound as the quantity of product increases. This is only realistic if the quantity produced is also the quantity sold. In other words, the model only works if the company sells everything it produces. The concept of demand takes into account the fact that in order to sell a certain quantity of product, the price must be adjusted accordingly. A demand function relates the price (dollars per item) to the quantity sold (items). In order to be consistent with our other functions, we will make the quantity sold the independent variable and the price the dependent variable. We will often call the demand function the price function or the price-demand function because of this. Suppose for a company that the price (demand) function is given by p(q) = - 0.3q + 824. 1. If the company chooses to produce 1277 items, what price should it charge in order to sell all of them? places. dollars per item. If necessary, round to two decimal 2. If the company sets the price to be $297.37 per item, how many can it expect to sell? items. If necessary, round to the nearest whole number. In this scenario, the price is NOT a set price. It varies depending on the quantity. So, unless we know the quantity produced, we cannot write a single number for the price. We write price as an expression involving q. This is given by the demand function. PRICE = – 0.3q + 824 Remember that the revenue function is PRICE times QUANTITY. So, we can find the revenue function by multiplying the demand function by q. 3. Write a formula for the revenue function for this company. R(q) =
Transcribed Image Text:The graph of the profit function in the last problem looks like this: This indicates that the company's profit grows without bound as the quantity of product increases. This is only realistic if the quantity produced is also the quantity sold. In other words, the model only works if the company sells everything it produces. The concept of demand takes into account the fact that in order to sell a certain quantity of product, the price must be adjusted accordingly. A demand function relates the price (dollars per item) to the quantity sold (items). In order to be consistent with our other functions, we will make the quantity sold the independent variable and the price the dependent variable. We will often call the demand function the price function or the price-demand function because of this. Suppose for a company that the price (demand) function is given by p(q) = - 0.3q + 824. 1. If the company chooses to produce 1277 items, what price should it charge in order to sell all of them? places. dollars per item. If necessary, round to two decimal 2. If the company sets the price to be $297.37 per item, how many can it expect to sell? items. If necessary, round to the nearest whole number. In this scenario, the price is NOT a set price. It varies depending on the quantity. So, unless we know the quantity produced, we cannot write a single number for the price. We write price as an expression involving q. This is given by the demand function. PRICE = – 0.3q + 824 Remember that the revenue function is PRICE times QUANTITY. So, we can find the revenue function by multiplying the demand function by q. 3. Write a formula for the revenue function for this company. R(q) =
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