A bakery makes two products

MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

A bakery makes two products, cakes

(x)

and pastries

(y)

, each requiring flour and sugar. The daily availability and requirements are: • Each cake needs

200\,\text{g}

flour and

100\,\text{g}

sugar. • Each pastry needs

100\,\text{g}

flour and

150\,\text{g}

sugar. • At most

4\,\text{kg}

of flour and exactly

3\,\text{kg}

of sugar are available per day. • The bakery accepts only whole products and must produce at least

5

pastries to meet standing orders. (i) Formulate all constraints as linear inequalities in

x

and

y

. (ii) Sketch the feasible region on the

xy

–plane, clearly indicating which boundary lines are solid and which are dashed. (iii) List the coordinates of the vertices of the feasible region.