A Polish company manufactures a technically advanced special detail. The selling price for this detail is 300 . The company can produce max. 12,000 units of detail per month. Last month, the company had a capacity utilization of 68% and a total cost of 1,380,000. This month, the company was able to increase its utilization rate to 90%. The total costs then amounted to 1,520,000. a) Determine the company's cost function, including their total fixed costs and variable costs per unit. (6 p) b) Calculate the company's critical volume. (3 p) c) Calculate the company's utilization rate at the critical volume. (2 p) d) The forecast for next month shows a utilization rate of 92%. How big will then be (i) the total gross margin (4 p) and (ii) the company's profit (2 p)? e) How does the critical point change if the number of units sold should fall? (1 p)