Question

DeWitt’s Widgets have fixed costs of $1.65 million and also have to spend $9.95 for each widget they produce.
The function W(p) = 2000000(EXP)-0.005p gives the number of items that Dewitts Widgets produces and also the number of items that they sell when they charge p, dollars per widget

What is the the price that would allow the company to break-even.
Write a complete factual sentence to interpret the value

Answer 1

Let price to breakeven be p

Number of widgets produced = 2000000e^-0.005p

Total Costs = Fixed Cost + Variable Cost = 1650000 + 9.95*2000000e^-0.005p

Total Revenue = p*2000000e^-0.005p

To breakeven , Total Costs = Total Revenue

=> 1650000 + 9.95*2000000e^-0.005p = p*2000000e^-0.005p

=> (p-9.95)*2000000e^-0.005p = 1650000

=> (p-9.95)e^-0.005p = 0.825

Solving for p gives us p = $10.82

Hence, each widget should be sold for $10.82 so that the company breaks even i.e. no profits and no loss. In this scenario, costs of production is equal to the revenue from sales.