Question

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)

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

Answer 1

(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.