XYZ Ltd is introducing a new product. The company intends to hire machinery to manufacture the product at a cost of $\$ 200,000$ per annum. However, this will only enable 60,000 units per annum to be produced, although additional machines can be hired at $\$ 80,000$ per annum. Each machine hired enables capacity to be increased by 20,000 units per annum, but it is not possible to increase production beyond 90,000 units because of shortage of space.

The minimum rental period is for one year and the variable cost is estimated to be $\$ 6$ per unit produced. There are no other fixed costs that can be specifically traced to the product. Marketing management has estimated the maximum selling prices for a range of output from 50,000 units to 90,000 units. The estimates are as follows:

* At $\$ 15$ demand will be in excess of 90,000 units but production capacity will limit the sales.

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Units sold Selling price ($) 50,000 60,000 70,000 80,000 90,000 90,000* 22 20 19 18 17 15