As newly appointed special advisor to the CEO of Cotton & Wool Industries, you a

Question

As newly appointed special advisor to the CEO of Cotton & Wool Industries, you are thinking about optimal production volumes of knitting wools. Knitting wools are some of the company's best selling products. Cotton & Wool Industries imports high quality, colored knitting wools in large bundles from Asia, transports the wool to their plant in Europe, cuts and re-packages them into smaller units and sells them to the end consumer via their web shop.

Part 1: Cost

Cutting and repacking the wool runs on a dedicated machine. Your colleague from bookkeeping tells you Cotton & Wool Industries incurs 611 Euros cost per day running the machine and cutting and packing the wool costs 33 Euros per ton.

Write an expression to calculate daily cost.

Part 2: Demand

You want to estimate the daily demand of wool depending on the selling price. You expect that increasing the price of wool by one Euro will reduce the demand by 2.94 tons a day. If you set the price to zero you assume that you can sell 49 tons of wool per day.

Write an expression for the daily demand of processed wool as a function of the selling price.

Use p to indicate the selling price in Euro per ton. Do not put any currency symbols into your answer.

Part 3: Revenue

Revenue from selling wool can be modeled by multiplying demand and selling price. From the previous questions, we have an expression for demand as a function of selling price.

Use the answer from the previous question to find an expression for the daily revenue generated from selling wool as a function of the selling price. (Use p to indicate the selling price in Euro per unit.)

Part 4: Cost to Manufacture

Because you are only going to re-package wool if you can sell it to customers, you can model production cost depending on demand. For example, if you expect Zunits to be sold given the price you set, you will produce Zunits.

Write an expression for the total daily cost of cutting and re-packaging wool as a function of the selling price. (Use p to indicate the selling price in Euro per unit.)

Part 5: Profit

Cotton & Wool Industries’ profit from selling cutted and re-packaged wool is the difference between revenue and manufacturing cost.

Write an expression for the daily profits gained from selling wool as a function of the selling price.

Explanation / Answer

1.

Fixed cost = 611 Euros

Variable cost = 33 Euros per ton

Daily total cost = 611 + 33Q

Here, Q = wools (in tons)

2.

When P = 0, Q = 49

Further, 2.94 ton of quantity demanded decreases, with increase in price of 1 euro and vice versa.

Then

Q = 49 – 2.94P

Here, Q = quantity demanded

3.

Revenue = P*Q

Then

Revenue = P*(49 – 2.94P)

Revenue = 49P – 2.94P^2

4.

Total daily cost = 611 + Z*P

5.

Profit = revenue – cost

Profit = 49P – 2.94P^2 – (611 + Z*P)

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