Question below:

Question

The demand equation for a certain product is given by p = 116 - 0.07x, where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R = xp.

Determine prices p that would yield a revenue 9160 dollars.

Lowest such price = ________

Highest such price = ________

Answer 1

R = xp = x(116 - 0.07x) = 9160; 0.07x² - 116x + 9160 = 0; x = (58 ±√(58² - 641,2))/0.07 = (58 ± 52)/0.07;

x = (58 + 52)/0.07 = 1543 or x = (58 - 52)/0.07 = 86

Lowest such price p = 116 - 0.07·1543 = $8 per unit

Highest such price p = 116 - 0.07·86 = $110 per unit