Question

1.

Suppose that the daily cost, in dollars, of producing xtelevisions 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 ofincreasing production to 63 televisions daily.

Round to the nearest dollar.

A) $5673
B) $5667
C) $5481
D) $5635

2.

A company estimates that the daily revenue (in dollars) from thesale of x cookies is given by:

R(x) = 885 + 0.02x + 0.0003x²

Currently, the company sells 900cookies per day.

Use marginal revenue to estimatethe increase in revenue if the company increases sales by onecookie per day.

A) $0.56
B) $56.00
C) $0.92
D) $92.00

3.

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 = $1.00; C'(50) = $1.00
B) ?C = $1.81; C'(50) = $1.80
C) ?C = $1.81; C'(50) = $1.30
D) ?C = $1.81; C'(50) = $1.00

4.

A company finds that when it spends x million dollars onadvertising, its profit P, in thousands of dollars, is given by

P(x) = 970 + 15x - 4x²

Currently the company spends 17 million dollars onadvertising.

Use the marginal profit to estimate the change in profit if thecompany increases its advertising expenditure by one milliondollars.

A) 255 thousand dollars
B) 119 thousand dollars
C) -121 thousand dollars
D) 970 thousand dollars

5.

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) $66
C) $55
D) $125

6.

Suppose that the weekly profit, in dollars, of producing andselling x cars is

P(x) = 0.006x³ - 0.3x² + 960x - 900

and currently 60 cars are produced and sold weekly.

Use P( 60) and the marginal profit when to estimate the weeklyprofit of producing and selling 61 cars.

Round to the nearest dollar.

A) $55,269
B) $56,083
C) $55,182
D) $55,183

7.

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 areproduced and sold per week.

Use the marginal profit toestimate the increase in profit if the store prodcues and sells oneadditional case of soup per week.

A) $7.29
B) $3877.00
C) $5.08
D) $5.52

8.

The weekly profit, in dollars, from the production and sale of xbicycles is given by

P(x) = 40.00x - 0.005x²

Currently, the company producesand sells 800 bicycles per week.

Use the marginal profit toestimate the change in profit if the company produces and sells onemore bicycle per week.

A) 48.00 dollars
B) 32.00 dollars
C) 40.00 dollars
D) 20.00 dollars

9.

A company estimates that the daily cost (in dollars) ofproducing x chocolate bars is given by

C(x) = 1635 + 0.02x + 0.0004x²

Currently, the company produces600 chocolate bars per day.

Use marginal cost to estimate theincrease in the daily cost if one additional chocolate bar isproduced per day.

A) $0.62
B) $0.50
C) $62.00
D) $50.00

10.

The profit, in dollars, from the sale of x compact disc playersis P(x) = x3 -8x2 + 9x + 7

Find the marginal profit when x = 10.

A) $149
B) $297
C) $290
D) $156