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Consider cach scenario: high-speed passenger train in Europe completes 900 km trip in hours. The train travels the first 600 km at an average speed that was 120 km/...

Question

Consider cach scenario: high-speed passenger train in Europe completes 900 km trip in hours. The train travels the first 600 km at an average speed that was 120 km/h faster than the last 300 km of the trip. If x represents the average speed of the train on the second part of the trip, then an equation to represent this situation is: 600 300 r+[20Identify all restrictions On the variable x in this context; (2 marks)Kailey is making earrings to sell at the local market: She spends S75 on supplies

Consider cach scenario: high-speed passenger train in Europe completes 900 km trip in hours. The train travels the first 600 km at an average speed that was 120 km/h faster than the last 300 km of the trip. If x represents the average speed of the train on the second part of the trip, then an equation to represent this situation is: 600 300 r+[20 Identify all restrictions On the variable x in this context; (2 marks) Kailey is making earrings to sell at the local market: She spends S75 on supplies and decides keep pairs of earrings to give to her friends Kailey sells the rest of the earrings she made for 5225, making profit of S11 per pair of earrings_ If n represents the number of pairs of earrings Kailey made; then an equation that represents this informalion IS: 225 75 MI= n-3 Identify all restrictions on the variable in this conlext (2 marks)



Answers

The production supervisor at Alexandra's Office Products finds that it takes 3 hours to manufacture a particular office chair and 6 hours to manufacture a computer desk. A total of 1200 hours is available to produce office chairs and desks of this style. The linear equation that models this situation is $3 x+6 y=1200,$ where $x$ represents the number of chairs produced and $y$ the number of desks manufactured.
a. Complete the ordered pair solution $(0,)$ of this equation. Describe the manufacturing situation that corresponds to this solution.
b. Complete the ordered pair solution $(, 0)$ of this equation. Describe the manufacturing situation that corresponds to this solution.
c. Use the ordered pairs found above and graph the equation $3 x+6 y=1200$
d. If 50 computer desks are manufactured, find the greatest number of chairs that they can make.

So we're told that tickets for a particular flight are $215, each. The plane seats 120 passengers, but the airline will overbook will purposely sell more than 120 tickets because not every paid passenger will end up showing up. So we're going to have D. Denotes the number of tickets the Arab line is going to sell and will assume that the number of passengers that actually show up for the flight X, follows a distribution. Um So ultimately we want to write the program to simulate the scenario um and we know that they wish to determine the optimal value. So running our program, we record the average profit from each run and it appears that the target value T. Is going to equal 142 tickets. So that would be our final result. Once we develop that program.

Okay. Here. Fixed cost is $45,000 and ah, variable cost days $80. So that X is equal to the number off pair. So we're total variable Cost is 80. Multiply by X right now cause function is given by total variable cost plus fixed costs. So your total variable cost is 80 x and our fixed causes $45,000. So this is Thea. Our cost function and your cost function is a linear function. So to grab the line, we need only two points. So your Y intercept is 45,000. So our first point is zero and 45,000. And ah, when X is a call to 300 then ah, cost is ah, $69,000. So we need to draw a line between these two points. Right now you're selling price is 255 per pair. Right. So your revenue function is given by price multiplied by quantity and here quantity is given by ex. Your revenue function is 255. Multiply by X. Now your revenue function is also linear function. So here we have also needed to points. So our first point is 00 because when X is equal to zero, then revenue is zero. Now, when number off bears are 300 which means when X is equal to 300 revenue is 76,000 and 500 right. So again, we need to draw a line between these two points. Now, profit function is given by the revenue minus cost. Your revenue is 255 x and cost is 80 x plus 45,000. Okay, here to 55 minus 80. That is equal to 1 75 x. So this is the our profit function, which is also linear functions to here. We need only two points to grab the line. So let X is a call to oh 300 when X is equal to 300 pairs than profit is 7500 and ah, when X is equal to 400 pairs than our prophet is 25,000. So to grab the profit function, we need to draw a line between these two points. Now, grab all these three functions once they maxus. So here are well, the red line that engaged your cost function and This is our two points. And here Blue Line is our revenue function and that this green line is our profit function. Right? Okay, so here we win. Sorry. You want to find a profit or loss when the X is equal to 3000 pairs? So our profit function waas p o fax is the Col Du 1 75 x minus 45,000. Now so too did the value off X and here X is equal to 3000. Okay, here 1 75 multiplied by 3000. That is a call to fight 25,000 minus 45,000. And that is they called you 4 80,000. So here are sign off for 80,000 is positive. Which means if we sell 3000 pairs, then we will get a profit off for $80,000. Okay. Now, to wreck even take p off X is a call to zero and your be off X is 1 75 x minus for sorry, 45,000. Now subject 1 75 outside. Therefore, X is equal to 257.14 So it is a proximate to 258. Now to break you won. The company must sell 250 years pays off. Skase. So this is your answer Number E. Thank you.

Okay. Here. Fixed cost is $45,000 and variable cost is $80. So that X is equal to the number off pair. So we're total variable Cost is 80. Multiply by X right now cause function is given by total variable cost plus fixed costs. So your total variable cost is 80 x and our fixed causes $45,000. So this is Thea. Our cost function and your cost function is a linear function. So to grab the line, we need only two points. So your Y intercept is 45,000. So our first point is zero and 45,000. And ah, when X is a call to 300 cost is $69,000. So we need to draw a line between these two points. Right now you're selling price is 255 per pair. Right. So your revenue function is given by price multiplied by quantity and here quantity is given by ex. Your revenue function is 255. Multiply by X. Now your revenue function is also linear function. So here we have also needed to points. So our first point is 00 because when X is equal to zero, then revenue zero. Now, when number off bears are 300 which means when X is equal to 300 and revenue is 76,000 and 500 right? So again, we need to draw a line between these two points. Now, profit function is given by the revenue minus cost. Your revenue is 255 6 and cost is 80 x plus 45,000. Okay, here to 55 minus 80. That is equal to 1 75 6. So this is the our profit function. We did also linear functions to here. We need only two points to grab the line. So let X is equal to 300 when X is equal to 300 pairs than profit is 7500. And ah, when X is equal to 400 pairs than properties 25,000. So to grab the profit function, we need to draw a line between these two points. Now, grab all these three functions on same access. So here are, uh, the red line that indicates your cost function, and this is our two points. And here are blue Line is our revenue function and that this green line is our profit function. Right? Okay, so here we win. Sorry. We want to find a profit or loss when the X is equal to 3000 pairs. So our profit function waas p off X is the Col Du 1 75 x minus 45,000. Now so too did the value off X and here X is equal to 3000. Okay, here 1 75 multiplied by 3000. That is a called a fight 25,000 minus 45,000. And that is they called you 4 80,000. So here are sign off for 80,000 is positive. Which means if we sell 3000 pairs, then we will get a profit off for $80,000. Okay. Now, to wreck even take p off X is equal to zero and your be off X is 1 75 x minus for 3. 45,000 no subject 1 75 outside. Therefore, X is equal to 257.14 So it is approximately 258 now to break even, the company must sell 250 years pays off space. So this is your answer number E

Okay, so here for part A um we have the linear cost function represents, the cost is going to be cfx and that is going to get to produce X. X necklaces during a one month period. That's going to be equal to just 3.5 times X. And then plus 604 year. Mhm. All right. So there we have our function C of X. And for part B it is then given that we are going to sell the necklace for $25 each. So therefore the revenue is just going to be 25 times X. So our X is going to be equal to 25 X. And then for part C we have the r minus C. Of X. O. R minus C of X is equal to our of X minus C. Of Excel. Therefore it's going to be equal to 25 X minus 3.5 X plus 6 40. Which then is going to evaluate here to 21 0.5 X 25. X minus 2.5 X. And then the minus 6 40 so minus 6 40. And therefore here r minus C. F. X. Is the profit such that the cost is subtracted from the revenue. So ar minus cfx here represents the profit for selling necklaces. So all the profit. Mhm. Mhm. For selling mixes. Yeah And for parity. Um well the profit then if the artist sells 212 necklaces is just substituting in 212 into 21.5 X -640. So we have 21.5 times 212 And then -640 and that's going to give us 3,918. Therefore the profit for selling 212 necklaces is going to be $3,918. Take care. Yeah.


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