Answer: p is approximately 1169.712
Step-by-step explanation:
To find the price at which the demand and total cost are equal, we need to set the demand function equal to the total cost function and solve for q.
Given the demand function p = -7q + 1165 and the total cost function c = 45q + 1200, we can set them equal to each other:
-7q + 1165 = 45q + 1200
Now, let's solve for q.
Add 7q to both sides of the equation to eliminate the -7q term:
1165 = 52q + 1200
Subtract 1200 from both sides of the equation:
-35 = 52q
Divide both sides of the equation by 52:
q = -35/52
Now that we have the value of q, we can substitute it back into either the demand or total cost function to find the corresponding price. Let's use the demand function:
p = -7q + 1165
p = -7(-35/52) + 1165
p = 245/52 + 1165
p = 4.712 + 1165
p ≈ 1169.712
