Answer :
Final answer:
To find the prices that yield a revenue of $6,510, one must solve the quadratic equation derived from the demand equation and total revenue formula, then substitute the number of units back into the demand equation to find the prices.
Explanation:
To determine the prices p that would yield a revenue of $6,510, we first use the given demand equation p = 130 - 0.035x, where p is the price of the product and x is the number of units produced.
To find the total revenue R, we multiply the price by the number of units, R = xp.
To find x for a given revenue, we substitute R with $6,510 and solve the equation $6,510 = x(130 - 0.035x).
Multiply out the right-hand side of the equation: $6,510 = 130x - 0.035x^2
Rearrange to form a quadratic equation: 0.035x^2 - 130x + 6,510 = 0
Use the quadratic formula to solve for x
Once we find the value of x, plug it back into the demand equation to find the corresponding price p that would yield a revenue of $6,510.
