You are a newly appointed consultantto KNIT'ting Industries and yourtask it to plan optimal production volumes of knitting wools. Knitting wools are some of the company's best selling products. KNIT'tingIndustriesimports 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 website.

Cutting and repacking one of their wool varieties, SKU B59, takes place on a dedicated machine. Your colleague, Justin, from bookkeeping tells you KNIT'ting Industries incurs 544 Euros cost per day running the machine and cutting and packing the wool costs 35 Euros per ton.

1- Write an expression to calculate the daily cost.

You want to estimate the daily demand of wool, SKU B59, depending on the selling price. You expect that increasing the price of wool by one Euro will reduce the demand by 1.36 tons a day. If you set the price to zero, you assume that you can sell 33 tons of wool per day.

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

Revenue from selling wool, SKU B59, 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.

3- 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.

Because you are only going to re-package wool, SKU B59, if you can sell it to customers, you can model production cost depending on demand. For example, if you expect "Z" units to be sold given the price you set, you will produce "Z" units.

4- Write an expression for the total daily cost of cutting and re-packaging wool as a function of the selling price

KNIT'ting Industries' profit from selling this cut and re-packaged wool, SKU B59, is the difference between revenue and manufacturing cost.

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