Question

Digital Cameras

The cost and revenue equations for a company that sells digital cameras are given by
R(x) = x(125 -0.0005x)
And
C(x) = 3.5x + 185000
Where R and C are measured in dollars and x represents the number of cameras sold. How many
cameras must be sold to obtain a profit of at least $6,000,000?

Answer 1

283,957 cameras

Explanation:

Profit generated = cost - Revenue

Given

Cost function C(x) = 3.5x + 185000

Revenue function R(x) = x(125 -0.0005x)

Profit = $6,000,000

To get the value of x, we will substitute the given parameters into the formula as shown;

$6,000,000 = 3.5x + 185000 - x(125 -0.0005x)

$6,000,000 = 3.5x + 185000 - 125x +0.0005x²

0.0005x²-121.5x + 185000 - 6,000,000 = 0

0.0005x²-121.5x-5815000 = 0

On solving the resulting quadratic equation

x = 283,956.91736581 and -40956.917365805

Ignoring the negative value, the minimum camera that must be sold is approximately 283,957 cameras