Question

1) The marginal cost function associated with producing x widgets is given by

C'(x)= -0.8x+75

where C'(x) is measured in dollars/unit and x denotes the number of widgets. Find the total cost C(x) incurred from producing the 11th through 05th units of the day.

The options are:

2040

2030

2020

2000

2050

a) The Math Club has determined that in order to successfully tutor x Math 2 students in preparation for the second homework, the price per student p(x) in dollars that must be charged/demanded is p(x)=180-3x

the club also determines that the total cost of tutoring x students is given by C(x)=7x+30

What price p(x) should they charge each student in order to maximize their profit?

Options are 93.5

143.5

98.5

68.5

43.5

Answer 1

(1)

we are given marginal cost as

we can find total cost

now, we can solve each integrals

and combine them

...........Answer

(2)

Price:

Revenue:

R(x)=xp

Cost equation:

now, we can find profit

G(x)=R(x)-C(x)

now, we can find derivative

now, we can set it to 0

and then solve for x

now, we can find price

..............Answer