The elements of the graph of P(x) provides information on the values of P(x) when different quantities of jackets are made and sold
First part; The company's profit will be exactly $0 if it makes and sells;
B. 20 or 70 (jackets)
Second Part; The company will make a profit if it makes and sells between 20 and 70 jackets;
B. Between 20 and 70
Third Part; But will not make a profit if it makes and sells more than 70 jackets
C. More than 70
Reason:
First Part
The given function is presented as follows; P(x) = -0.0005·(x² + 30)·(x - 30)·(x - 70)
Where;
P(x) = The weekly profit
Two factors of the function P(x) are (x - 30) and (x - 70), therefore, at x = 30, and x 70, the company's profit will be exactly $0.
However, from the graph, the value of the profit function, P(x) is zero when x = 20 and x = 70
Therefore,
The correct option is B. 20 or 70
Second Part;
From the graph of the function, the value of the profit P(x) (profit is made) is positive in the domain 20 ≤ x < 70
Therefore, the company will make profit if makes and sells between (20 and 70) jackets
The correct option is B. Between 20 and 70
Third Part
From the graph of the function, the value of P(x) is negative when x > 70
Therefore, the company will not make profit if it makes and sells (More than 70) jackets
The correct option is C. More than 70
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