A company produces and sells two products A and B, x units of product A and y units of product B. The price obtained when selling x units of product A, p, is: p= 400–1.5x-y, The price obtained when...

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Extracted text: A company produces and sells two products A and B, x units of product A and y units of product B. The price obtained when selling x units of product A, p, is: p= 400–1.5x-y, The price obtained when selling y units of product B, is: q = 450-x-2y. The total costs of producing and selling x units of product A and y units of product B are: TC(x, y) = 100x+50y+0.5x +y +10000. Show that the company's profit function can be written as: 7(x,y) = -2x-2xy-3y + 300x + 400y-10000. b) Calculate the first order partial derivatives of z(x.y), and find the only stationary point. Show that the stationary point of r(x, )is a local maximum point and calculate the maximum profit. Due to constraints on capacity, the company has to produce exactly 70 units of the two products altogether. Calculate how many of cach product A and B the company now must produce to maximise its profit. d) Calculate the size of the maximum profit given the constraints