I have everything right but the last question asking how many cases per week

The consumer demand equation for tissues is given by
q = (97 − p)2,
where p is the price per case of tissues and q is the demand in weekly sales.
(a) Determine the price elasticity of demand E when the price is set at $34. (Round your answer to three decimal places.)
E = 1.079

Interpret your answer.

The demand is going ? down by 1.079 % per 1% increase in price at that price level.

(b) At what price should tissues be sold in order to maximize the revenue? (Round your answer to the nearest cent.)
$ 32.33

(c) Approximately how many cases of tissues would be demanded at that price? (Round your answer to the nearest whole number.)
? cases per week

To determine the number of cases of tissues demanded at the price that maximizes revenue, we need to find the price that maximizes revenue first. Here's how to solve it step by step:

Step 1: Recall the revenue equation:
Revenue = Price * Quantity

Step 2: Express the quantity in terms of price using the demand equation:
q = (97 − p)^2

Step 3: Substitute the quantity expression into the revenue equation:
Revenue = Price * (97 − p)^2

Step 4: Expand the equation:
Revenue = Price * (97^2 − 2 * 97p + p^2)

Step 5: Simplify by multiplying the terms:
Revenue = Price * (9409 − 194p + p^2)

Step 6: Differentiate the revenue equation with respect to price:
d(Revenue)/dp = 9409 − 194p + p^2 − 194p

Step 7: Set the derivative equal to zero to find the maximum:
0 = 9409 − 194p + p^2 − 194p

Step 8: Simplify the equation and solve for p:
0 = 9409 − 388p + p^2
0 = p^2 − 388p + 9409
Using the quadratic formula, we find two possible values for p: p = 194 ∓ sqrt(194^2 - 4*9409)

Step 9: Calculate the values of p:
p1 = 194 + sqrt(194^2 - 4*9409) ≈ 194 + 140.34 ≈ 334.34
p2 = 194 - sqrt(194^2 - 4*9409) ≈ 194 - 140.34 ≈ 53.66

Step 10: Since the price cannot be negative, we discard p2 and consider p1 as the price that maximizes revenue.

Therefore, tissues should be sold at approximately $334.34 to maximize revenue.

To find the corresponding quantity demanded, substitute the price back into the demand equation:

q = (97 − 334.34)^2
q ≈ (-237.34)^2
q ≈ 56292

So, approximately 56,292 cases of tissues would be demanded per week at the price that maximizes revenue.