3. Location Choice There is a new tech company \"Humbl\

3. Location Choice There is a new tech company "Humbl", with a single consumer market in town A. Humbl uses two inputs, these are obtained from respectively the cities B and C, which are 600 kilometers apart. The distance between A and B, and between A and C is 500 kilometers. Humbl can sell its output in A at a price of $100 per unit. In order to produce one unit of output, they need two units of inputs from B and three units of input from C. The cost of one unit of input from B is $5. For a unit input from C the cost is $10. The costs for the transportation of the finished product from the site of production to A are zero. The transport of one unit of input from B costs $2 per 100 kilometers, and the transportation costs for one unit of C $3 per 100 kilometers. a. b. c. d. Give a graphical representation of the situation described above by drawing the Weberian triangle as accurately as possible. A situation where the (variable) cost of transporting finished products are zero (or negligible), is exceptional. Give an example of a product of which the variable costs of transportation to the consumer market are negligible. Give a mathematical description of the production function of "Humbl". What makes this production function so special? Determine the optimum location for "Humbl" and determine the transport costs and profits in the optimal location. Provide a graphical illustration.