Question

A dietician has to develop a special diets using two foods X and Y. Each packet (containing 30g) of food. X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Y contains 3units of calcium , 20 unit of iron, 4 units of cholesterol and 3 units of vitamin A.The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are

• A. (2,72), (40,15), (15,20)
• B. (0,23), (40,15), (2,72)
• C. (2,72), (15,20), (0,23)
• D. (2,72), (40,15), (115,0)

Answer 1

The Correct Option is A

Let the quantity of food X used as x packets and the quantity of food Y used as y packets.
The constraints can be represented as follows: 
\(12x + 3y ≥ 240\) (constraint for calcium) \(4x + 20y ≥ 460\) (constraint for iron) \(6x + 4y ≤ 300\) (constraint for cholesterol) 
To find the corner points, we solve these constraints as a system of linear inequalities. 
First, let's plot the feasible region on a graph: 

The constraints can be rearranged to isolate y: 
\(y \geq \frac{240 - 12x}{3}\) (constraint for calcium) 
\(y \geq \frac{460 - 4x}{20}\) (constraint for iron) 
\(y \leq \frac{300 - 6x}{4}\)(constraint for cholesterol) 
By plotting these inequalities on a graph, we can find the corner points where the feasible region intersects. 
After graphing, we find that the corner points of the feasible region are approximately (2, 72), (40, 15), and (15, 20). 
Therefore, the correct option is (A) (2, 72), (40, 15), (15, 20).