Question

Let C(q) represent the cost and R(q) represent the revenue, in dollars, of producing q items.

Answer 1

Answer:

(a)$4954

(b)$10

(c)The company should not produce the 101st item.

Step-by-step explanation:

(a)

$C'(50)=\dfrac{C(52)-C(50)}{52-50} \\\\C(50) = 4900,C'(50) = 27\\\\ Therefore:\\27=\dfrac{C(52)-4900}{52-50}\\C(52)-4900=27*2\\C(52)=4900+54\\C(52)=\ 4954$

(b)If C'(50) = 27 and R'(50) =37

• Cost will increase by $27
• Revenue will increase by $37

Therefore, the profit earned on the 51st item

$=R'(50)-C'(50)$

=37-27

=$10

(c)If C'(100) = 41 and R'(100) =37

• Cost will increase by $41
• Revenue will increase by $37

Therefore, the profit earned on the 101st item

Profit $=R'(100)-C'(100)$

=37-41

=-$4

The company should not produce the 101st item. It would lose $4 if it does.