Suppose the Delta Company a fine producer of widgets has hired you as a consultant. The cost, demand and revenue functions have been determined By Delta and given below. The total amount of widgets sold in the market by all producers, including Delta's sales, is 238 units. Delta's current price is $80 with sales of 10 units which gives Delta a market share of approximately 0.04201 or 4.201%. You have been asked to answer the following questions, part A and B.

P=$100-2Q Demand for Deltas Widgets

TC=Q2+2Q+100

A) Determine Delta Company's output that minimizes cost per unit (ATC), the optimal price at this output and level of profits. Be sure to show whether your solution is a maximum or a minimum. 

B) Determine Delta Company's profit maximizing output (round output to a whole number), the optimal price at this output and level of profits. Be sure to show whether your solution is a maximum or a minimum.10. 

C) If Delta wants to increase their market share to .05 or 5% what price and level of output will achieve this goal assuming that the rest of the industry's sales do not change. At this new price and output calculate Delta's profit.

Note: When you are asked to forecast a quantity resulting from a change in a variable you may use the definition of elasticity, the easy method, to derive the forecast for all problems.