A company manufactures two models of toy cars, Model X and Model Y. The model X,...

   

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A company manufactures two models of toy cars, Model X and Model Y. The model X, the most affordable, sells for 1 euro each. As for the Y model, which is much more sophisticated, it sells for 3 euros. The manufacturing cost, expressed in euros, is given by the following function C(x,y)=5x+5y2-2xy-2x-1000. where x is the number of model X toy cars and y is the number of model Y toy cars. It is assumed that the manufactured toys are all sold on the market. Throughout the exercise, we note C+= (R1) 1) Let (x, y) E C.. Determine the P(x, y) profit made by the company when it 1. Soit (x, y) 2 C+. Determine the profit P(x, y) made by the firm when it sold x model toys X a model toys Y. ANSWER 1): 2) Investigate the convexity of the function P in C+. ANSWER 2): A company manufactures two models of toy cars, Model X and Model Y. The model X, the most affordable, sells for 1 euro each. As for the Y model, which is much more sophisticated, it sells for 3 euros. The manufacturing cost, expressed in euros, is given by the following function C(x,y)=5x+5y2-2xy-2x-1000. where x is the number of model X toy cars and y is the number of model Y toy cars. It is assumed that the manufactured toys are all sold on the market. Throughout the exercise, we note C+= (R1) 1) Let (x, y) E C.. Determine the P(x, y) profit made by the company when it 1. Soit (x, y) 2 C+. Determine the profit P(x, y) made by the firm when it sold x model toys X a model toys Y. ANSWER 1): 2) Investigate the convexity of the function P in C+. ANSWER 2):