I need help please show work A firm produces a product that

I need help, please show work

A firm produces a product that has the production cost function C(x)-390x+15,340 and the revenue function R(x) 520x. No more than 26 units can be sold. Find and analyze the break-even quantity, then find the profit function The break-even quantity is 118 units Type a whole number.) If the company can produce and sell no more than 26 units, should it do so? O A. Yes. Since 26 is less than the breakeven quantity, production of the product can produce a profit. B. No. Since 26 is equal to the break-even quantity, production of the product cannot produce a profit. XC. Yes. Since 26 is greater than the break-even quantity, production of the product can produce a proft. D.No. Since 26 is less than the break-even quantity, production of the product cannot produce a profit Write the profit function Px)-

Solution

Production function is C = 390x + 15340. Revenue function = 520x. The value of x cannot exceed 26.

At the break even point, profit is zero. Hence R - C = 0

520x - 390x - 15340 = 0

130x = 15340

This gives x = 118.

Now when it sells at most 26 units, profit is R - C or 520*26 - 390*26 - 15340 = -11960.

Hence it should not produce anything because the break even quantity is quite higher and profits are not going to occur below it. Hence Option D is correct

P(x) = R(x) - C(x) or is given by P(x) = 130x - 15340