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For a certain company, the cost function for producing x items is C(x)=50x+250 and the revenuefunction for selling x items is R(x)=-0.5(x-90)2+4,050. The maximum capacity of the company is 110items.The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost functionC(x) (how much it spends). In economic models, one typically assumes that a company wants tomaximize its profit, or at least make a profit!Assuming that the company sells all that it produces, what is the profit function?====P(x)=Hint: Profit = Revenue - CostWhat is the domain of P(x)?Hint: Does calculating P(x) make sense when x-10 or x-1,000?The company can choose to produce either 40 or 50 items. What is their profit for each case, andwhich level of production should they choose?Profit when producing 40 items=Profit when producing 50 items=Can you explain, from our model, why the company makes less profit when producing 10 more units?

For A Certain Company The Cost Function For Producing X Items Is Cx50x250 And The Revenuefunction For Selling X Items Is Rx05x9024050 The Maximum Capacity Of Th class=

Sagot :

First, let's calculate the Profit functions which is P(x)=R(x)-C(x)

Let's continue simplifying the function

The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number

Domain=(-∞,∞)

Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.

And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.

Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):

The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.

The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.

According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function

As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.

View image LayoniS282047
View image LayoniS282047
View image LayoniS282047
View image LayoniS282047
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