Only answer part 2 The Apex Widget Company has determined th

Only answer part 2

The Apex Widget Company has determined that its marginal cost function is C\'(x) = 0.5x + 50, where x represents the number of boxes of widgets which can be produced each week and C is in dollars. The cost of producing 200 boxes of widgets is $22,500. Also, if they charge $50 per box, they will sell 350 boxes; and if they charge $75 per box they will sell 300 boxes. Assume this demand equation is linear. Find: (Assume that a box of widgets can be opened and divided before being shipped to a customer and that there are 120 widgets in a box.) the demand equation. the revenue function. the number of boxes which they should sell to maximize revenue. the maximum revenue. the (total) cost function. the average cost function. the production level (number of boxes) which yields minimum average cost. the minimum average cost. the profit function. the number of boxes which they should produce and sell to maximize profit. the maximum profit. the price which should be charged in order to maximize the profit. Suppose that boxes of widgets cannot be opened and divided before being shipped to customers. Which of your answers to the questions in Part 1. will be changed? Explain how. Find what the new answers to these questions will be.

Solution

The cost function is C(x) = 0.25x² + 50x + 500, and the demand function is D(x) = -2x + 450. where x is the number of boxes of widgets. Each box contains 120 widgets. From the demand function, it is apparent that the demand is for 120x widgets . If the number of widgets in a box changes, then the number of boxes will change in such a way as to keep 120x same. Thus, the demand equation will change, i.e. the answer to the question (a) will change.