An art teacher has to prepare exactly 3 litres of a violet shade by mixing red…
MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
An art teacher has to prepare exactly 3 litres of a violet shade by mixing red pigment and blue pigment. The pigments are poured in measures of exactly 0.5 litre each. Let x be the number of 0.5-litre measures of red pigment and y be the number of 0.5-litre measures of blue pigment.
(i) Establish the linear equation connecting x and y.
(ii) Draw the graph of the equation on a Cartesian plane, showing clearly where the line meets the axes.
(iii) Shade the region representing mixtures whose total volume does not exceed 3 litres.
(iv) The shade quality will be acceptable only if at least two 0.5-litre measures of blue pigment are used. Represent this additional requirement on the same graph.
(v) Using the completed graph, list all integral ordered pairs (x,y) that satisfy both conditions and hence state how many distinct acceptable mixtures can be prepared.