the inventor charges $4.00 per unit, then her profit for producing and selling x units is given by the function P(x) = 2.25x - 7000
(a) What is her profit if she sells 2000 units?
(b) What is per profit if she sells 5000 units?
(c) What is the break-even point for sales?
(a) Substitute 2000 for x in the equation for P(x). That will be the profit.
(b) ditto
(c) Set P(x) = 0 and solve for x. That is the number of sales needed to break even.
To find the profit if the inventor sells 2000 units, we can substitute 2000 for x in the equation for P(x) = 2.25x - 7000.
(a) P(2000) = 2.25(2000) - 7000
= 4500 - 7000
= -2500
Therefore, her profit if she sells 2000 units is -$2500.
To find the profit if the inventor sells 5000 units, we can substitute 5000 for x in the equation for P(x).
(b) P(5000) = 2.25(5000) - 7000
= 11250 - 7000
= 4250
Therefore, her profit if she sells 5000 units is $4250.
To find the break-even point for sales, we need to set P(x) = 0 and solve for x.
(c) P(x) = 2.25x - 7000
0 = 2.25x - 7000
2.25x = 7000
x = 7000 / 2.25
Therefore, the break-even point for sales is approximately 3111 units.