In the market for lock washers, a perfectly competitive market, the current equilibrium price is $5 per box. Washer King, one of the many producers of washers, has a daily short-run total cost given by TC = 190 + 0.20Q + 0.0025Q2, where Q measures boxes of washers. Washer King's corresponding marginal cost is MC = 0.20 + 0.005Q. How many boxes of washers should Washer King produce per day to maximize profit?

The number of boxes of washers Washer King should produce per day to maximize profit = 960 boxes.

And the corresponding maximum daily profit = $2,114

Explanation:

The daily, short-run total cost of producing Q boxes of the product is given as

TC = 190 + 0.20Q + 0.0025Q²

The unit price of the product = $5.

Total revenue = (Unit Price) × (Quantity sold) = 5Q

Profit = (Revenue) - (Total Cost)

Profit = 5Q - (190 + 0.20Q + 0.0025Q²)

Profit = P(Q) = -190 + 4.8Q - 0.0025Q²

To maximize the profits, we just obtain the point where the profit function reaches a Maximum.

At the maximum of a function, (dP/dQ) = 0 and (d²P/dQ²) < 0

Profit = P(Q) = -190 + 4.8Q - 0.0025Q²

(dP/dQ) = 4.8 - 0.005Q

At maximum point,

(dP/dQ) = 4.8 - 0.005Q = 0

Q = (4.8/0.005) = 960 boxes

(d²P/dQ²) = -0.005 < 0 (hence, showing that the this point corresponds to a maximum point truly)

Hence, the number of boxes of washers Washer King should produce per day to maximize profit = 960 boxes.

The corresponding maximum profit is then obtained from

P(960) = -190 + (4.8×960) - 0.0025(960²)

Maximum daily profit = $2,114

Hope this Helps!!!

the correct answer is economics is a game without winners or losers.

unlike sports or games economic is a game without losers or winner rather it is a game where everyone wins. parties of business doing businesses exchange money with each other and hence exchange is done on the basis of goods. one party takes the goods and other sales it so there is winner on both sides. each party values more highly the good it gets than the good it gives up. both sides exchange only because both intend to increase their value. so there is no concept of lose or win.