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Cost Function. The cost function for selling product is given asC(x) = 100 + 60 In(2x2 32x 200)where x is the number of units of 10,000 pounds sold. Find the number...

Question

Cost Function. The cost function for selling product is given asC(x) = 100 + 60 In(2x2 32x 200)where x is the number of units of 10,000 pounds sold. Find the number of pounds that should be sold to keep cost at a minimum. Include a graph of the cost function. Make sure you use calculus to answer the question:

Cost Function. The cost function for selling product is given as C(x) = 100 + 60 In(2x2 32x 200) where x is the number of units of 10,000 pounds sold. Find the number of pounds that should be sold to keep cost at a minimum. Include a graph of the cost function. Make sure you use calculus to answer the question:



Answers

Given the cost function $C(x)$ and the revenue function $R(x)$, find the number of units $x$ that must be sold to break even. See Example 6. $$ C(x)=75 x+160,000 R(x)=200 x $$

Problem. 56 in this problem to functions are given. The ex is equal to zero point it x last 900. Another function is odd. Eggs is equal to two weeks for the break. Even CX is equal to biotics now, substituting the Afghan functions 0.8 eggs less. 900 is equal to two x. This implies that 900 is equal to 1.2 eggs. Our X equal do 7 50 for the break even condition the value off exit 7 50

Of love. 53. In this problem cost functions see X is given US D X Plus 10,000 and have a new function. Rx is given as 46 x now for the break even condition c X Should we call to Odd X so we can write cardi X Less 10,000 is a call to 46 x. This will give us 10,000. Is it called tau 16 x or X equal to 625? This is the answer.

Problem Number 58 In this problem to functions are Gail. Our ex is equal. To who? Or by X and CX. Is it cool too? 105 X plus 7 +00 00 We have to find the value off X at break even at break even point biotics is equal to CX So we get right. Two for five X is equal to 105 x less 70,000. This will give us the value off X s five 100.

So we know it costs them to make these scooters, it costs them 20 times however many scooters plus 1000. And that's for however many scooters are going to produce and then we want to look at the price demands and what the price will be based on demand and that is 140 -2X. Where X. is From 0 to 70. So the maximum they'll make a 70. And let's find the profit equation. So how many you sell times how much you're selling them for less? The cost will give us our profit equation. And so that will be negative two X. Squared. And then we'll have 140 x -20 x. So they'll be plus 120 x. And then when we distribute here that will be -1000. So there's our profit equation and we want to find where that vertex is. And we know that this equation has a Y intercept down here at negative 1000. It's going to open downward and we're going to have it doing something like this. And this is what we want to find is where that maximum profit is. We also want to find these two points because they will be our break even points. So we know what negative B Over two A and two times this is -4. It looks like 30 is the number we want to sell. So 30 scooters and what will be the Profit that will make the capital t. for 30 is. And let's calculate calculate that negative two times 30 squared is 900 Plus 120 times 30 minus 1000. And so we would be making $800. Or they would be making $800 of profit. And how much would they sell each scooter for? Let's find that out. We'll use that linear equation. We'll take 140 -2. X. Yeah that is We would sell them for $80 each. So sell 30 scooters for $80 each and you'll end up making a profit of 800. Now let's find the last thing is that break even point which we would set dysfunction equal to zero. And I'm going to multiply. Well we'll just use it. We can multiply through by negative two. And make these divide by negative two. And then make all the numbers smaller. Well just use it as is so we have negative 1 20 plus or minus the square root of 120 square -4 times a times C all over to a which will be negative for now let's find out what that 1 20 squared -4 times. And then this will be 2000 and that comes out to be 6400. And so that comes out nicely that that is just 80. So we have negative 1 20 plus or minus 80 over negative four. So negative 1 20 plus 80 over negative four and negative 1 80 minus 80 over negative four. And so this is the negative negative 200 Over -4. So that's going to be 50. And then this one is gonna be negative 40 Over four which will be over negative for which will be 10. So let's look back at our picture. This is at 10, This is at 50. That's where we make zero profit. That's a break even point. Any time we sell from 11 to 49 you're going to make profit. But the best is to have 30 because that will maximize your profit.


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