Part 1: Transportation Cost

On a Friday night, you are sitting in the office preparing for a meeting with a logistics service provider,Mark, for next week. Last-mile delivery costs are a concern for KNIT'ting Industries. You are wondering if you can estimate a service provider's transportation cost for a dedicated area. A textbook suggests that daily logistics cost (in Euros) for an area(in square-kilometers) can be estimated as follows:

-22 * d + 3 *d^2 + 191

Mark says his daily costs to serve an area are 211 Euros.

Calculate the area (in square kilometers) that the logistics provider covers with the cost using the equation above.

*Round your answer to two decimal places (e.g. if the result is 1.534 put in as an answer 1.53).

Part 2: Transportation Cost (cont'd)

Consider the logistics cost equation given in Part 1 to answer the following question.

1. The function is concave for d>0
2. The function is concave for negative values of d
3. The function is convex
4. The function is concave
5. We can not say if the function is concave or convex

Part 3: Special Applications

KNIT'ting Industries also has innovative applications for the industry. One of their applications include developing color baths for knitting wools. The color baths are mixed using two different ingredients - the color and an agent that makes the color more UV stable. Other ingredients go into the color baths that are not important to the analysis. The mix of the two ingredients depends on the product type (knitting wool variety).

Consider two products SKU W41 (Product A) and T38 (Product B). You are asked to calculate the 'amount of blue color bath' for Product A and Product B. The following table indicates the amount of blue color (in liters) and UV agent (in liters) needed to prepare one litre of Product A and one litre of Product B.

	Product A	Product B
Blue Color (in liters)	0.172	0.441
UV agent (in liters)	0.425	0.26

Suppose you have to prepare the blue color baths for Product A and Product B at the same time. You have 300 liters of blue color and 536 liters of UV agent available. How many liters of Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

Round your result to two decimal digit.

1- Amount of Product A?

2- Amount of Product B?

Part 4: Total Production Cost

Some customers in KNIT'ting Industries' B2B business can order larger quantities of colored wool. For this special order product the company assumes that economies of scale are present. The operations department head, Daniel, tells you that they currently estimate thetotal production costto produce an order of sizewith the formula:

TC(q) = a * q^b

wherea>0andb>0.

The operations department tells you that the total cost of a B2B-order isTC=589 if the order volume isq=29. They assume that the parametera=24 .

1- Find the value of parameter.

Round your result down to three decimal digits. For example, if your result is 2.3215 put in 2.322