Can someone please help me with this assignment? The weekly profit, in dollars,
ID: 2841160 • Letter: C
Question
Can someone please help me with this assignment?
The weekly profit, in dollars, from the production and sale of x bicycles is given by
P(x) = 40.00x - 0.005x2
Currently, the company produces and sells 800 bicycles per week.
Use the marginal profit to estimate the change in profit if the company produces and sells one more bicycle per week.
A) 32.00 dollars
B) 20.00 dollars
C) 48.00 dollars
D) 40.00 dollars
A company estimates that the daily cost (in dollars) of producing x chocolate bars is given by
C(x) = 1635 + 0.02x + 0.0004x2
Currently, the company produces 600 chocolate bars per day.
Use marginal cost to estimate the increase in the daily cost if one additional chocolate bar is produced per day.
A) $0.62
B) $50.00
C) $0.50
D) $62.00
A company estimates that the daily revenue (in dollars) from the sale of x cookies is given by:
R(x) = 885 + 0.02x + 0.0003x2
Currently, the company sells 900 cookies per day.
Use marginal revenue to estimate the increase in revenue if the company increases sales by one cookie per day.
A) $56.00
B) $92.00
C) $0.56
D) $0.92
The profit, in dollars, from the sale of x compact disc players is P(x) = x3 -8x2 + 9x + 7
Find the marginal profit when x = 10.
A) $290
B) $149
C) $156
D) $297
A grocery store estimates that the weekly profit (in dollars) from the production and sale of x cases of soup is given by
P(x) = -5600 + 9.5x - 0.0017x2
and currently 1300 cases are produced and sold per week.
Use the marginal profit to estimate the increase in profit if the store prodcues and sells one additional case of soup per week.
A) $5.52
B) $3877.00
C) $5.08
D) $7.29
The total cost, in dollars, to produce x DVD players is C(x) = 70 + 7x - x2 + 2x3
Find the marginal cost when x = 3
A) $136
B) $55
C) $66
D) $125
Suppose that the daily cost, in dollars, of producing x televisions is
C(x) = 0.003x3 + 0.1x2 + 62x + 620
and currently 60 televisions are produced daily.
Use C(60) and the marginal cost to estimate the daily cost of increasing production to 63 televisions daily.
Round to the nearest dollar.
A) $5673
B) $5481
C) $5635
D) $5667
For the total-cost function
C(x) = 0.01x2 + 0.8x + 50
find ?C and C'(x) when x = 50 and ?x = 1
A) ?C = $1.81; C'(50) = $1.80
B) ?C = $1.81; C'(50) = $1.00
C) ?C = $1.81; C'(50) = $1.30
D) ?C = $1.00; C'(50) = $1.00
A company finds that when it spends x million dollars on advertising, its profit P, in thousands of dollars, is given by
P(x) = 970 + 15x - 4x2
Currently the company spends 17 million dollars on advertising.
Use the marginal profit to estimate the change in profit if the company increases its advertising expenditure by one million dollars.
A) 255 thousand dollars
B) 119 thousand dollars
C) -121 thousand dollars
D) 970 thousand dollars
let me know if you require more points
Explanation / Answer
All the questions are of the same kind. For example if the cost involved in making a shoe is $30 and making 2 shoes is $40. Then the marginal cost involved in making the second shoe is $40-$30 = $10. Considering this we can solve the problems.
Q1. On producing 800 bicycles, the company makes a profit of (40*800)-(0.005*800^2) = 28800. If one more bicycle is produced, then profit would be (40*801)-(0.005*801^2) = 28831.995. So marginal profit is 28831.995-28800 = 31.995 = 32 dollars.
Q2. For 600 chocolates, cost is 1635 + 0.02*600 + 0.0004*600^2 = 1791
For 600 chocolates, cost is 1635 + 0.02*601 + 0.0004*601^2 = 1791.5. So marginal cost is $0.5
Q3. For 900 cookies, revenue is 885 + 0.02*900 + 0.0003*900^2 = 1146
For 901 cookies, revenue is 885 + 0.02*901 + 0.0003*901^2 = 1146.56. Marginal revenue is $0.56
Q4. For x=10, differentiate P(x) = x3 -8x2 + 9x + 7 and put x=10.
On differentiation, we get 3x^2-16x+9 = $149
Q5. weekly profit of 1300 cases = -5600 + 9.5*1300 - 0.0017*1300^2 = 3877
weekly profit of 1301 cases = -5600 + 9.5*1301 - 0.0017*1301^2 = 3882.078. So marginal profit is $5.08
Q6. differentiate 70 + 7x - x2 + 2x3 and put x=3 for marginal cost. We get 7-2x+6x^2. On substitution x=3, we get $55
Q7. C(60) = 5348. C(63) = $5673.04. (By sustituting x=63 in the equation.)
I'll answer the remainig questions in the comments.