Memphis plc is a multi-division firm operating in a wide range of activities. One of its divisions, Division A, produces a semi-finished product Alpha, which can be sold in an outside market. It can also be sold to Division B, which can use it in manufacturing its finished product Beta. Assume also that the marginal cost of each division is a rising linear function of output, and that the goal for Memphis plc is to maximize its total profits.
Relevant information about both divisions is given below.

You are required to calculate the optimal transfer price for Alpha and the optimal activity level for each division. 

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Revenue from Total cost outside selling of Alpha Output of Alpha (units) of Alpha (000) (000) Net marginal revenue of Beta (000) 60 112 315 47 70 140 350 45 80 170 380 43 90 203 405 40 100 238 425 36 110 275 440 33 120 315 450 30 130 359 455 25