Question

A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?

190

likes
951 views

Answer to a math question A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?

Expert avatar
Timmothy
4.8
97 Answers
To minimize the total costs, you should find the number of licenses you need to sell to cover the fixed costs and the variable costs per license. In this case, the cost function can be represented as follows: Total Cost (C) = Fixed Costs + (Variable Cost per License) * (Number of Licenses Sold) Fixed Costs = $5,000 Variable Cost per License = $50 Let's denote the number of licenses to be sold as "x." We want to minimize the total cost, so we need to find the value of "x" that minimizes the total cost. The total cost function is: C(x) = $5,000 + $50x Now, to minimize the total cost, set up a cost equation where the total cost equals the revenue, which is the product of the number of licenses sold and the selling price (assuming that you're selling each license for a certain price "p"): C(x) = p * x Now, you need to find the price "p" that covers both the fixed and variable costs. Substituting the values: $5,000 + $50x = p * x Now, you want to isolate "x" to find the number of licenses to sell. Start by subtracting $5,000 from both sides: $50x = p * x - $5,000 Now, factor out "x" from the right side: $50x = x(p - $5,000) Now, divide both sides by "x": $50 = p - $5,000 Add $5,000 to both sides: $5,050 = p So, you should sell each license for at least $5,050 to cover both the fixed and variable costs. The number of licenses you need to sell to minimize the total costs is not influenced by the selling price; it remains "x."

Frequently asked questions (FAQs)
Question: What is the equation of the logarithmic function that passes through the point (2, 3) and has a vertical asymptote at x = 5?
+
What is the area of a rectangular prism with length 5 cm, width 6 cm, and height 8 cm?
+
Question: What is the variance of the data set {5, 8, 12, 15, 18, 20, 24}?
+
New questions in Mathematics
The gross domestic product the gdp for the United States in 2017 was approximately $2.05x10^3. If you wrote this number in standard notation , it would be 205 followed by how many zeros
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____
Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)
Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years? Round your answer to the nearest cent.
What is the r.p.m. required to drill a 13/16" hole in mild steel if the cutting speed is 100 feet per minute?
-0.15/32.6
The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers
A circular window has a rubber molding around the edge. If the window has a radius of 250 mm, how long is the piece of molding that is required ? (To the nearest mm)
How to do 15 x 3304
You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations): Overheads R 176,200 Cost of capital (% of purchase price per annum) 11.25% Annual License Fees—Truck R 16,100 Driver Monthly cost R 18,700 Assistant Monthly cost R 10,500 Purchase price: - Truck R 1,130,000 Depreciation: straight line method Truck residual value 25% Truck economic life (years) 5 Purchase price: Trailer R 370,000 Tyre usage and cost (c/km) 127 Trailer residual value 0% Trailer economic life (years) 10 Annual License Fees—Trailer R 7,700 Fuel consumption (liters/100km) 22 Fuel price (c/liter) 2053 Insurance (% of cost price) 7.5% Maintenance cost (c/km) 105 Distance travelled per year (km) 48000 Truck (tyres) 6 Trailer (tyres) 8 New tyre price (each) R 13,400 Lubricants (% of fuel cost) 2.5% Working weeks 50 Working days 5 days / week Profit margin 25% VAT 15% Q1. Calculate the annual total vehicle costs (TVC)
The function h(t)=-5t^2+20t+60 models the height in meters of a ball t seconds after it’s thrown . Which describe the intercepts and vertex of this function
What is 75 percent less than 60
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?
x²-7x+12=0
To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³
Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.
An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?
In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.