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 ?(?) = 2000000 ? − 0.055 ? gives the number of widgets that the market is demanding. (This gives the number of items that DeWitt’s Widgets produces and also the number of items that they sell when they charge ? dollars per widget. DeWitt’s produces items on demand.)

1. In this problem you will identify formulas for total cost incurred by DeWitt’s Widgets. (a) The formula for the total cost of the company would make, ?(?), when making W widgets is: ?(?) = 1650000 + 9.95(?). Briefly explain how this formula was found. (b) The formula for the total cost of the company would make, ?(?), when charging ? dollars per widget is: ?(?) = 1650000 + 9.95(2000000 ? − 0.055 ? ). Briefly explain how this formula was found. 3

2. Use Excel to solve for the price that would allow the company to break-even. Write a complete sentence to interpret this value using correct context.

3. Estimate the price DeWitt’s should charge to create the highest profit in the given interval. Identify the approximate profit they will earn when charging that price. Explain how you arrived at your estimate.

Answer 1

According to the question:

Demand : ?(?) = 2000000 ? − 0.055 ?

fixed costs of $1.65 million

Variable cost : $9.95 for each widget they produce.

a) Total cost : ?(?) = 1650000 + 9.95(?)

Total cost is the cost incurred to produce a particular good in this case widget. It is the sum of fixed cost which does not var in short run such as investment in machinery, building and is independent of good produced and variable cost which changes depending on the good produced and factor of productions such as labor, fuels, materials.

b) Now, ?(?) - 1650000 + 9.95(2000000 ? − 0.055 ? ) : This is the total cost of quantity demanded W(p) -2000000 ? − 0.055p. Fixed cost - 1650000 and Variable cost - 9.95(2000000 ? − 0.055 ? ).

c) Break even: TR = TC

TC = 1650000 + 9.95(2000000 ? − 0.055 ? )

TR = p* ?(?) = p*(2000000 ? − 0.055 ?)

p*(2000000 ? − 0.055 ?) =  1650000 + 9.95(2000000 ? − 0.055 ? )

Note I used value of e = 2.71828

Solving this: we get

p=

49423268

q=	2718280

Break-even point is the point after which firm won't be able to cover its variable cost. This p will at least make firm to cover its variable cost,

c) Please specify the interval.