Question 1 Suppose the sunglasses Hut Company has a profit function by P(q)= -0

Question 1 Suppose the sunglasses Hut Company has a profit function by P(q)= -0.03q² + 4q -32, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses.

A) Find a simplified expression for the marginal profit function. (BE sure to use the proper variable in your answer.)

MP (q) = -------------------

B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.)

Answer: ---------------------thousand pairs of sunglasses need to be sold.

C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to thee decimal places.)

Answer: ---------------------- thousand dollars of maximum profits can be expected.

Question 1

The Function f(x) = -2x³ + 27x² – 48x + 4 has one local minimum and one local maximum.

This function has a local minimum at x = ------

With value ------------------

And a local maximum at x = -------

With value -------------

Question 2

Consider the function f(x) = x⁴ – 72x² + 6, -5 ≤ x ≤ 13.

This function has an absolute minimum value equal to ---------------

And an absolute maximum value equal to --------------

Question 3

Let f(x) = (5+x)⁴

F(x) has one critical value at A = ----------------

For x < A, f(x) is [select an answer]

For x > A, f(x) is [select an answer]

Question 4

Consider the function f(x) = 12x⁵ + 75x⁴ – 120x³ + 5

F(x) has inflection points at (reading from left to right)x=D,E and F

Where D is --------------------

And E is -------------------------

And F is -------------------------

For each of the following intervals, tell whether f(x) is concave up or concave down.

(- ∞, D):  [select an answer]

(D, E):      [select an answer]

(E, F):      [select an answer]

(F, ∞) :    [select an answer]

Question 6

Suppose a company’s revenue id given by R(q) = -q³ + 330q² and its cost function is given by C(q) = 540 + 17q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.

Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)

MP (q) = -----------

B) How many items (in hundreds) need to be sold to maximize profits? ( Round your answer to two decimal places.)

Answer : ---------------hundred unit must be sold.