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Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in dollars) will depend on the...

Question

Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. Probability Taste Design A Design B 0.20 conservative 190000 425000 0.50 no 'change 235000 435000 0.30 liberal 385000 305000 #oou decide to choo

Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. Probability Taste Design A Design B 0.20 conservative 190000 425000 0.50 no 'change 235000 435000 0.30 liberal 385000 305000 #oou decide to choose Design A for 80% of the production lines and the remaining 20% for Design B, what is the expected value of profit? (Keep whole dollarsh



Answers

The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean
400 dollars and standard deviation
20 dollars . If
450 dollars is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? a. Answer the question, using Table 4, Appendix 3. b. Applet Exercise Use the applet Normal Probabilities to obtain the answer. c. Why are the labeled values different on the two horizontal axes?

The question say is that we have immigration that is equal. Does the next plus five I minus 200. Your ex is number or long sleeved T shirts on by Is number off short sleeved the Shourd's Andi companies making profit that X at dollar then then and buy and dollar by So a. But we need to graph this plane. So this is a graph we will get. So it is having Rangers 02 30 a 60 here on the IT alliances. And this is the zero Texas coming up. There is no intersection of Zaid Aces B. Burgess to find that the company makes profit or blows. If excess 20 and vice, then it's a little substitute them, so that is equal to Ben Indoor 20 plus five into 10 minus 200. So I get 200 plus 50 minus 200 0 to 50. So therefore it is a profit, See, but says we need to find Exco Marie, which even the company breaks. Mark this it on a graph so way to find the value of X and y If there is 1/4 0 so zero is equal to panics. Bless. Bye bye Minus 200. So I get there Next, plus by very is a cool too tool 100. Does this to works place by is it will do 40. So this is the line safe X zero I get Why is for be on for by zero I get Xs 20. So it is Mark this on the ground. So if by zero Xs 20 this is a point. And if x zero by is for dessert, this is a point. So this is a lying off the graph bill company will make

In question 30 were asked to interpret the data that we plotted in question 28. So just to review that data represented the hourly wages of 25 employees. And the first part of question 30 asks. About 75% of the employees made less than what amount per hour. So key phrases, they're they're looking at 75% of the employers of the employees. So right there, we know we're talking, you know, about three of the cartons. And just to be careful, which three core tiles relic carefully at the phrase made less than says that less than is there. So So they were looking at them wages per hour. It's the question. So 75% made less than blank wages per hour. Okay, so that tells me I'm looking for this bottom 75%. Remember that each portion each quartile represents 25% of my data. No matter how they're spaced out and the blocks plot the court ALS of each place mark off 25% of my data. So 75% of my data lies to the left of the third quartile. Excuse me. 75% of my data lies to the left of the third quartile. So the question then is what was the wage? What's that Highest wage of all that lower 75%. So we look at that third quarter number, I'm going to get the exact number from over here on the left that was displayed by the class Calcutta AP. And so I see that I've got $17.65. So be careful to put your answer with a quirky units that this is money. So that was the the maximum wage made by 75% of the employees. Part B asks what percent of the manufacturers made more than $15.80 an hour. Well, I need to figure out where 15 80 is online on my chart, and I'll see I look over here. That that is my median value. So that's my second quarter value. Their $15.80. And so we know that represents the exact halfway point. So 50% less than that 50% of the employees make more than that. Um, this question was about which, what percent made more? The answer, of course. Still, 50% from part B. Part C is asking if you randomly select one person from all these 25 what is the likelihood that they made less than 15 80? So we're looking at the same benchmark place here. The median value of of hourly wage is $15.80 an hour, and they're using this phrase. What is the likelihood that one randomly selected person makes less than 15 80? Remember, likelihood is another way of saying What is the probability? And that's represented by the relative for sense. So we would still say there's a 50% chance that are randomly selected. Employee makes less than $15.80 an hour, and that's all for question 30.

You probably have been given a table of values and I'd like to find both the expected value and then the standard deviation, what the expected value is just equal to the sum of acts at times the probability events, what now? This is negative 15,000 times 0.5 because that's the probability of 15,000 plus zero times 0.15 plus 15,000 times the probability of 15,000, which is 0.15 plus 25,000 times 0.30 plus 40,000 times the probability of 40,000 which were given his 0.15 plus 50,000 times the probability of 50,000, just 0.10 Almost 100,000 times 2.5, 150,000 times point of three plus 200,000 times 0.2 It's And so to find the expected value, we just parted this in and then add them all together. And when we do this should give us are expected value is 33,000 500. Now to find the standard deviation, we need to know the expected value of X squared. Now to find that we just come up here and square all of our x values, not the probability values, but we just square all of our various x five and then we put this in just like we did on the last one and and there's all together, let me do this. It gives us the value of 26975 followed by 50 Now, that's an under standard deviation. Yeah, are variants is equal to the expected value of X squared minus the expected value of X squared, but our standard deviation is the square root of this. Yeah. As we're going to take the square root of the answer, we just got minus 33 500 squared because that was our expected value. And when we do, we get our standard deviation is 39,000. It's a 10 $89 and 42 cents

Alright. In this problem, we have a business owner who is looking to maximize her profit and we know some information about the prices. Sheikhoun sell her product her sweatshirts for in the quantities at which she can sell. And we know some information about her revenues and costs. So how we're going to approach this is go through and for each person quantity, we're gonna find the total revenue which will be priced times quantity, to see how much money she's bringing in from sales. And then we're going to find the total costs. And it's important to note that we have two different types of costs. We have a fixed cost of $1000 per week for her Web service. Then we have a marginal cost of $20 per sweatshirt being sold. So we have to make sure we're multiplying that marginal cost by the quantity and we're always adding on that fixed cost. So here's our equation for costs here, fixed cost plus marginal cost, times quantity and then once we have those, we confined our profit simply by subtracting all of our costs from all our revenue, and that will be our economic weekly profit. So I've got no started here. This first one is a little self explanatory. You're not going to make much of a profit because you're selling at a price of zero. Um, but to go through the process, we have that price. Times quantity for revenue will be zero, and we're still incurring costs because you have that fixed costs of $1000 a week and you still have to pay $20 for each sweatshirt. And our quality of sweatshirts is 100. So, um, 100 plus another 1000 plus 2000 or costs are 3000 zero minus 3000 are profit is negative 3000. You probably wouldn't want to operate in this situation. We'll keep going to see if that increases at a price of $20 you can sell 80 sweatshirts revenue price times quantity, 1600 in our costs, we still have a $1000 fixed cost. This time we're adding on our marginal cost of 20 times. 80 is our quantity. So 1000 plus 20 times 80 is 2600 as our costs, um so our revenue 1600 minus our costs 2600 give us a profit of negative 1000. So we're still operating at a loss here. So we'll move on to the next one at a price of 40 weaken cell 60 sweatshirts. So our revenue here will be priced times quantity 40 times 60. And that is a revenue of 2400, which is looking good Better than before andare costs. We still have our fixed costs of 1000. We still are marginal cost of 20. But we're gonna multiply that 20 now by 60 and we're going to get a total cost of 2200. We at that all together. And so we have revenue of 2400 cost of 2200. Our profit is now 200. So it's good we're in. The positives were making a profit, but we'll keep going to see if we can do better at a price of 60 Weaken sell 40. Our revenue is 60 times 40. Um, and so we're gonna get the same revenue is before we multiply those. It's gonna be 2400 for a revenue. But our costs will change because their quantity is changing. So we still that $1000 fixed cost, and we have that $20 marginal cost. But we're multiplying that by just 40 this time, Um, s O that means our cost will be 1000 plus 20 times 40 which gives us 1600 and so are our profit will be 2400, minus 1600 which gives us $600 of profit. That is looking good, but we'll keep going, just in case we can do even better. Um, at a price of 80 quantity is 20. So 80 times 20 gives us a revenue of 1600 and our costs will be 1000 for fixed costs plus marginal cost 20 times the quantity of 20. Um so that gives us 1400. And so our profit is again going down to 200 and it's always good to check. Do this last one. But I'm not gonna bother. It might not be totally worth your time because the quantity is zero. So it's gonna be kind of similar to that for a situation where you're not bringing in any revenue, but you still have cost, so you know you're gonna have a negative profit here. So now that we have all of our profits. We can look at where that is highest, and we can see that it is here when we're making an economic profit of $600 per week. So that is our total weekly economic profit. And that is that this profit maximizing point. So we can now define, um, this point where the price of each sweatshirt it's is $60 and the quantity sold is 40. These are our profit maximizing price and quantity, and again, economic profit is $600.


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