A small company manufactures a certain product. Variable costs are $20 per unit
ID: 1239074 • Letter: A
Question
A small company manufactures a certain product. Variable costs are $20 per unit and fixed costs are $10,875. The price-demand relationship for this product is P= -0.25D + 250, where P is the unit sales price of the product and D is the annual demand. Use the data (and helpful hints) that follow to work out answers.- Total cost = Fixed cost + Variable Cost
- Revenue = Demand X Price
- Profit = Revenue - Total Cost
Set up your graph with dollars on the y axis (between 0 and $70,000) and, on the x axis, demand D: (units produced or sold), between 0 and 1000 units.
a) Develop the equations for total cost and total revenue.
b) Find the breakeven quantity (in terms of profit and loss) for the product.
c) Find the profit that the company would obtain by maximizing it's total revenue and neatly graph the solutions
Explanation / Answer
(a) Develop equations for total cost and total revenue. Total Cost = Fixed cost + Variable cost = 10,875 + 20D Total Revenue = PD = (-0.25D + 250)D = -0.25D2 + 250D ================================== (b) Find the breakeven quantity (in terms of profit and loss) for the product. Breakeven, when Revenue = Cost OR Profit = 0 Profit = Total Revenue Total Cost = -0.25D2 + 250D (10,875 + 20D) = -0.25D2 + (250-20)D 10,875 Set Profit = 0 -0.25D2 + 230D 10,875 = 0 D = 50 or D = 870 B r e a k e v e n Q u a n t i t y = 50 o r 870 If you make less than 50 units, there will be a loss of money and if you produce more than 870 units, there will be a loss of money. ===================================================== (c) What profit would the company obtain by maximizing its total revenue? Total Revenue (TR) = PD = (250 Total Profit (0.25D)D = 250D 0.25D2 = -0.25D2 + 250D (10,875 + 20D) = -0.25*(500)2 + 250*500 (10,875 + 20*500) = $41,625