The cost and revenue functions for producing and selling x units of a product are given. cost and revenue are expressed in dollars. upper c (x )equals 75 x plus 84 comma 660 upper r (x )equals 245 x a. find the number of units that must be produced and sold to break even. at this level, what is the dollar amount coming in and going out? b. write the profit function from producing and selling x units of the product.

(A) the number of units produced and sold at break-even point is the value of X and that is 1.126 units.

(B) the dollar amount coming in and going out at this point/level is the price of X and that is 0.37 dollars

(C) the profit function for X units produced and sold is: π(x) = R(x) - C(x)

where pie (the symbol "π") represents PROFIT.

Step-by-step explanation:

(A) C(x) = 75x + 84 ...(equation 1)

660R(x) = 245x

R(x) = 245x ÷ 660 = 0.3712x

So R(x) = 0.3712x ...(equation 2)

To find X, equate the cost function to the revenue function

75x + 84 = 0.3712x

X = -1.126units

Since quantity cannot be negative in real life situation, we use the modulus of X in place of the above value.

|X| = 1.126 hence X = 1.126 now

Since we equated cost to revenue in order to get this quantity X, X is the quantity produced and sold at break even point.

Break-even point is the point where cost = revenue

This is also the point where profit is zero because profit = revenue - cost

(B) Revenue = Price × Quantity

R = P×Q

Our revenue here is 0.3712x

Which is equal to 0.418 dollars

So P = R÷Q

Price = 0.418÷1.126 = 0.37 dollars

(C) This is the profit function from producing and selling X units of the product: π(x) = R(x) - C(x)

4.5%

step-by-step explanation: