For xyz manufacturing the fixed costs are $1200, material and labor costs combined are $2 per unit, and the demand equation is:

p=100/√q

What level of output will maximize profit? Show this occurs when marginal revenue equals marginal cost. What is the price at the profit maximization?

see your previous post.

To find the level of output that maximizes profit, we need to equate marginal revenue with marginal cost. Then, we can substitute the resulting output value into the demand equation to find the corresponding price.

Let's break it down step by step:

1. Start by finding the marginal revenue (MR) function:
- The demand equation given is: p = 100/√q
- To find the revenue equation, multiply price (p) by quantity (q): R = p * q
- Take the derivative of the revenue equation with respect to quantity (q) to find the marginal revenue (MR).

2. Now, calculate the marginal cost (MC) function:
- The material and labor costs combined are $2 per unit, so the variable cost (VC) per unit will be $2.
- Fixed costs (FC) are given as $1200.
- The total cost (TC) equation can be written as: TC = FC + VC * q
- Take the derivative of the total cost equation with respect to quantity (q) to find the marginal cost (MC).

3. Set MR equal to MC and solve for the level of output (q):
MR = MC

4. Substitute the computed output value into the demand equation to find the price (p):
p = 100/√q

Let's go through the calculations:

1. Marginal Revenue (MR):
Revenue equation: R = p * q
Derivative of the revenue equation:
MR = dR/dq = dp/dq * q + p

Since p = 100/√q, we differentiate it with respect to q:
dp/dq = d(100/√q)/dq = -50/q^(3/2)

Substitute dp/dq into the MR equation:
MR = -(50/q^(3/2)) * q + p = -50q^(-3/2) + p

2. Marginal Cost (MC):
Total cost equation: TC = FC + VC * q
Derivative of the total cost equation:
MC = dTC/dq = d(FC + VC * q)/dq = d(1200 + 2q)/dq = 2

3. Set MR equal to MC:
-50q^(-3/2) + p = 2

4. Solve for q:
-50q^(-3/2) = 2 - p
q^(-3/2) = (2 - p)/50
Taking the reciprocal and raising to the power -2/3:
q = [(2 - p)/50]^(-2/3)

Now, substitute the value of q into the demand equation to find the price (p):

p = 100/√q
p = 100/√[(2 - p)/50]^(-2/3)

Unfortunately, at this point, we cannot solve for the exact value of the price without numerical approximations or further simplification.

However, we have obtained an expression for the level of output (q) that maximizes profit. To find the price at profit maximization, you can plug in the value of q into the demand equation or use numerical methods to find an approximate value.