5. A firm has two plants (A) and (B) for production. The Total cost function for each is given by: TCA = 12 + 7QA- 2QA2 + 0.72QA3 and TCB = 5 + 3QB + 1.5QB2 where TCA and TCB are total costs and QA and QB are quantity produced from each plant. The firm wishes to minimize the cost of producing any given amount of product. It is also known that in allocating the products to the two plants, the firm must produce 20 bags. Find the minimum values of QA and QB and confirm that the cost is minimised

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