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Jane manages a small bakery that bakes only make-to order cakes. Her total cost (TC) and total revenue (TR) functions are as follows: TC =

Jane manages a small bakery that bakes only "make-to order" cakes. Her total cost (TC) and total revenue (TR) functions are as follows:

TC = 50 + 80Q - 10Q2 + Q3

TR = 100Q - 8Q2

The bakery has a capacity of handling 30 units at any one time.

  1. Determine the price she should charge if she wants to maximise total revenue.
  2. Compute the price she should charge if she wants to maximise profits.

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