Suppose the sunglasses hut company has a profit function given by p ( q ) = − 0.02 q 2 + 5 q − 30 , 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) Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) The actual maximum profits that can be expected is 180 thousands dollars.

Step-by-step explanation:

Given : Suppose the Sunglasses Hut Company has a profit function given by

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.

To find :

A) How many pairs of sunglasses (in thousands) should be sold to maximize profits?

Profit is

Compare with general quadratic equation

a=-0.02, b=4, c=-20

The maximum value of quadratic function is at

So, maximum profit occur at q is given by,

i.e. 100 thousand pair of sunglasses.

Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) What are the actual maximum profits (in thousands) that can be expected?

Maximum profit occurs at q=100 thousand pairs is given by,

The actual maximum profits that can be expected is 180 thousands dollars.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.