Question

An electronics store sells 70 digital cameras per month at a price of $320 each. For each $20 decrease in price, about 5 more cameras per month are sold. Use the verbal model and quadratic function to determine how much the store should charge per camera to maximize monthly revenue.

Answer 1

The amount that the store should charge per camera to maximize monthly revenue is; $300

From the model revenue equation, we have;

Revenue = Price × Sales

Now, Let R(x) represent revenue

Thus;

R(x) = (320 - 20x)*(70 + 5x)

Expanding this gives us;

R(x) = -100x² + 200x + 22400

Since the coefficient of x² is negative, it will be a downward opening parabola and thus the vertex will be at a maximum. Hence, we can use axis of symmetry formula to find x. Which is;

x = - b/2a

x = -200/(-2 x 100)

x = - 200/-200

x = 1

Thus the price to maximize revenue monthly will be gotten by plugging in 1 for x into (320 - 20x)

So, Price = (320 - 20(1))

Price = $300

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