(ii) The profit function, in dollars, for a product is given by Π(x) = −x3 + 76x2 − 380x − 2800, where x is the number of units produced and sold. If break-even occurs when 10 units are produced and sold, (a) Find a quadratic factor of Π(x).(b) Find a number of units other than 10 that gives break-even for the product.

(a) The factors are (x + 4), (10 - x) and (x - 70).

(b) There is a break-even for 70 units of the product.

Step-by-step explanation:

(a)

Factorizing the term in parentheses,

Then

The factors are (x + 4), (10 - x) and (x - 70).

(b)

Break-even occurs when Π(x) = 0

or or

Since x cannot be negative, x = 70.

Hence, there is a break-even for 70 units of the product.

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

42

step-by-step explanation: