A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/Kg of vitamin C. It costs Rs 50 per kg to produce food I. Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C and it costs Rs 70 per kg to produce food II. Formulate this problem as a LPP to minimise the cost of a mixture that will produce the required diet. Also, find the minimum cost.
Let the dietician mix x Kg of food I & y Kg of food II.
To minimize:
subject to constants:
corner points value of
500
380 minimum
560
since the feasible region is bounded. so 380 may or may not be the minimum value of Z. To check,Let
Note that the feasible region and do not have any common point
value of z is Rs 380 when x= amount of food I=2 Kg and y=amount of food II=4 Kg