Suppose that you can sell as much of a product (in integer units) as you like at $60 per unit. Your marginal cost (MC) for producing the qth unit is given by: MC=7q This means that each unit costs more to produce than the previous one (e. g., the first unit costs 7*1, the second unit (by itself) costs 7*2, etc.). If fixed costs are $80, what is the profit at the optimal integer output level?

Profit at the optimal integer output level is $176.50.

Explanation:

This can be determined as follows:

Step 1: Calculation of optimal integer output level

At the optimal integer output level, profit is maximized where marginal revenue (MR) is equal to the marginal cost (MC), i.e. where;

MR = MC (1)

For any product, the MR is equal to the price per unit of the product. Therefore, we have:

MR = Price per unit = $60

Also given,

MC = 7q

Substituting for MR and MC in equation (1) and solve for q, we have:

$60 = 7q

q = $60 / 7

q = 9 units

Therefore, the optimal integer output level is 9 units.

Step 2: Calculation of total revenue at optimal integer output level

Total revenue = Price per unit * q = $60 * 9 = $540

Step 3: Calculation of total cost at optimal integer output level

Since MC = 7q, the total cost (C) can be obtained by taking the integral of the MC as follows:

C = ∫(MC)dq = ∫[7q]dq = (7 / 2)q^2 + F = 3.5q^2 + F (2)

Where F is Fixed cost which is given as $80.

We then substitute F = $80 and q = 9 into equation (2) to have:

C = 3.5(9^2) + 80

C = (3.5 * 81) + 80

C = 283.50 + 80

C = $363.50

Therefore, total cost at the optimal integer output level is $363.50.

Step 4: Calculation of profit at optimal integer output level

Profit = Total revenue - Total cost (3)

Where;

Total revenue = $540; from step 2 above.

Total cost = $363.50; form step 3 above.

Substituting the values into equation (3), we have:

Profit = $540 - $363.50 = $176.50

Therefore, profit at the optimal integer output level is $176.50.

support your answer using the data presented. (5 points). 4. based on the information you used to schedule and curve, which product would you recommend the shoe hut focus on, and why? provide details that support your answer. (5 points).

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30