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3. A firm is considering setting up a vending machine to sell its products on a university campus. There is no substitute available at present on campus. No other firms selling similar products are expected to enter the campus in future. The firms initially incurs a setup cost of $100 that cannot be recovered. The only other cost of the business is the cost of the product material at $10 for each product sold. Demand function of its product on the campus is estimated to be P = a - Q. Q is quantity sold and P is the price. (a). Calculate the profit-maximization price and quantity and the maximized profit level. (b). Calculate the minimum value of a that the firm is willing to enter the campus. (c). Having set up the vending machine on the campus, the firm soon discovers it overestimates the demand. The true value of a is 20. Will the firm withdraw from the campus? Explain with reference to the answer in (b)