BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles Binôme : Anglais / Mathématiques Sujet 6 LINEAR PROGRAMMATION The first part of this page is a summary that can help you to do the exercise.
An ordered pair (a, b) of real numbers is solution of an inequality in x and y if the substitution x = a and y = b satisfies the inequality. For example, the ordered pair (2,5) is a solution of y < 2 x + 3 because 5 < 2 × 2 + 3 , that is to say 5 < 7. However, the ordered pair (2,8) is not a solution because is obviously wrong . The graph of an inequality in x and y consists of all pairs (x,y) that are solutions of the inequality. The graph of an inequality involving two variables is a region of the xy-plane. The point (2,7) is on the graph of the line y = 2 x + 3 but is not a solution of y < 2 x + 3 . A point (2,y) below the line y = 2 x + 3 is a solution of y < 2 x + 3 . The graph of y < 2 x + 3 is the set of all points below the line y = 2 x + 3 . EXERCISE A costume jewellery store is going to close down. The manager wants to get rid of the leftovers. He has in stock 54 necklaces, 36 bracelets and 116 rings. To sell these goods, he decides to sell off by batches. Batch A includes 6 necklaces, 2 bracelets and 10 rings. It is sold for 60£. Batch B includes 2 necklaces, 4 bracelets and 12 rings. It is sold for 40£. Let x be the number of batches of type A. Let y be the number of batches of type B. 1) Write down three inequalities satisfied by x and y. 2) Using the following figure, shade the unwanted region corresponding to these inequalities.
4) a) If E is the turnover in pounds for the sale of x batches A and y batches B, prove 3 E . that y = − x + 2 40 b) Draw the line ∆ whose equation is 3 E y =− x+ for E = 200. 2 40 c) ( x0 , y 0 ) is the ordered pair that gives the highest turnover. Explain how to obtain (x0 , y 0 ) graphically. Give the corresponding turnover. Is the stock exhausted?
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