The profit (in millions of dollars) from the sale of x million units of Blue Glue is given by p= .7x-25.5. The cost is given by c= .9x +25.5
(a) Find the revenue equation.
(b) What is the revenue from selling 10 million units?
(c)What is the break-even point?
To find the revenue equation, we first need to understand that revenue is calculated by multiplying the number of units sold (x) by the selling price per unit. Since the selling price per unit is not explicitly given, we need to derive it using the profit and cost equations.
(a) The revenue equation can be found by rearranging the profit equation p = 0.7x - 25.5. We know that profit is equal to revenue minus cost, so we can express the revenue as p + c.
Substituting the given cost equation c = 0.9x + 25.5, we have:
Revenue (R) = p + c = (0.7x - 25.5) + (0.9x + 25.5)
Simplifying, R = 1.6x
Therefore, the revenue equation is R = 1.6x.
(b) To find the revenue from selling 10 million units, simply substitute x = 10 into the revenue equation:
R = 1.6(10) = 16 million dollars.
So, the revenue from selling 10 million units is 16 million dollars.
(c) The break-even point occurs when the revenue equals the cost, i.e., R = C. In this case, we can set the revenue equation R = 1.6x equal to the cost equation C = 0.9x + 25.5 and solve for x.
1.6x = 0.9x + 25.5
0.7x = 25.5
x = 25.5 / 0.7
Therefore, the break-even point occurs when approximately 36.43 million units are sold.