Answer:
(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)
