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A firm produces two types of products, A and B. The number of items produced in each product are x (for Product A) and y (for Product B) respectively. The firm is subject to cost constraints: Product A should cost $4 each and Product B should cost $6 each. The total cost of both products should be equal to $1,250 to maximise the profit. The firm's associated profit functionis 7 = 15x 24y + 7x? + 4.5y? (a) Determine the equation of the constraint based on the firm's requirements. (b) Use Lagrange multipliers to determine the number of each product needed to be sold to maximise the profit. (c) Find the maximum profit subject to the given constraint