Step-by-step explanation:
(a)
the cost function is
C(x) = 300 + 20x
(b)
the revenue function is
R(x) = 35x
(e)
the profit function
P(x) = R(x) - C(x) = 35x - 300 - 20x = 15x - 300
(d)
break-even is the point where C(x) and R(x) are equal :
C(x) = R(x)
300 + 20x = 35x
300 = 15x
x = 300/15 = 20
so, the break-even is only achieved when 20 units are produced and sold. and with more than 20 sold units the business would then make a profit.
per our restrictions only max. 19 units can be sold, so, the business will always be in the negative numbers (unless they cheat and sell virtual units that were never produced).
therefore, the product should not be produced at all.
