1 answer

I am not sure if all information is correct. I need help with numbers 5-9 Doubling...

Question:

Doubling Production. In general, the costs for doubling production of any type of item are expected to decrease by approximat
5) une con Page 2 of 2 Plot the scatter plot of the equation and the line that represents the cost of producing a thousand Bo

I am not sure if all information is correct. I need help with numbers 5-9
Doubling Production. In general, the costs for doubling production of any type of item are expected to decrease by approximately 25% per item. If we know that the costs for producing 10,000 Bouncy Balls is $1500, and if costs decrease by 25% for each item when production is doubled, determine the cost equation for producing x thousand Bouncy Balls. 1) What is the cost per item when 10,000 Bouncy Balls are produced? 1506/10 000 Cost per item is is cents 2) What is the cost per thousands of items when 10,000 Bouncy Balls are 1500/10 produced? Cost per thousands of items when 150 10,000 Bouncy Balls are Produced is $150. 3) Fill in the table of values below and use the results to find the cost equation. Cost * (thousand) Bouncy Balls 10 = 2°. 10 20 = 2.10 40 = 22.10 80 = 2.10 160 = 24.10 x = 2 .10 Calculation for Cost of Production #items. Cost per Item 10 • ( ) = 1500 20 (150 x 40 (150X (4 30 (150x2 1600150x 3/4 " O C/56x35 1500 23.30 3375 Soc2.5 7593.25 4) In order to fill in the last row of the table, you will need to solve the following equation for y: x=2". 10. Give the solution to the equation. n = _(log x-1)/(0.3010)
5) une con Page 2 of 2 Plot the scatter plot of the equation and the line that represents the cost of producing a thousand Bouncy Balls. Is this a logarithmic equation, an exponential equation, or neither? Explain your reasoning? 6) Use the equation to determine intercept for the cost function and interpret its meaning. Is it possible to estimate the fixed cost of production? If so, give an estimate. 7) Give an appropriate domain and range for the cost function. When does the cost model become ineffective? a) What is an appropriate domain? b) What is an appropriate range? 8) Use the model to determine how many Bouncy Balls can be produced at a cost of $10,000. 9) According to your model, how much would it cost to produce 120,000 Bouncy Balls? Soluti Symbolic

Answers

(5) The curve can be shown as below. The equation is exponetial in nature as it uses exponents for calculations.

16000 y = 42.691x + 1345.6 14000 12000 10000 Cost 8000 6000 4000 0 50 100 250 300 350 150 200 Output

(6) A linear function can be used to estimate the equation as cost = 1345.6 + 42.691 (x) as shown in the diagram above. i.e., Y-intercept = 1345.6. Even when there is no production cost equals 1345.6, which can also be interpreted as the fixed cost.

(7) The domain of the function is (0, +infinite) which denotes the values of x that is feasible and the range is (1345.6, + infinite), which denotes the range of values the function can take.

(8) At a cost of 10,000, using the linear equation, we get x = (10000 - 1345.6)/42.691 = 202.7 (approximately).

Hence, approximately 202 bouncy balls can be produced with 10,000.

(9) When x = 120,000 we get cost using the linear equation as C = 1345.6 + 42.691 (120) = 6468.52.

Hence, it would cost 6468.52 to produce 120,000 bouncy balls.

.

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