In a test of Mathematics, there are two types of questions to be answered-short answered and long answered. The relevant data is given below Type of questions Time taken to solve Mark s Number of question Short answered questions 5 minute 3 10 Long answered questions 10 minute 5 14 The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except x ≥ 0 , y ≤ 0 , are

Question

In a test of Mathematics, there are two types of questions to be answered-short answered and long answered. The relevant data is given below <table class="table table-bordered "> Type of questions Time taken to solve Mark s Number of question Short answered questions 5 minute 3 10 Long answered questions 10 minute 5 14 The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except x ≥ 0 , y ≤ 0 , are (A) 5x + 10y ≤ 180 , x ≤ 10 , y ≤ 14  (B) x + 10y ≥ 180 , x ≤ 10 , y ≤ 14  (C) 5x + 10y ≥ 180 , x ≥ 10 , y ≥ 14  (D) 5x + 10y ≤ 180 , x ≥ 10 , y ≥ 14

Tardigrade Admin · Accepted Answer

Obviously x ≤ 10, y ≤ 14 and 5x + 10y ≤ 180

$5 x + 10 y \leq 180, x \leq 10, y \leq 14$

$x + 10 y \geq 180, x \leq 10, y \leq 14$

$5 x + 10 y \geq 180, x \geq 10, y \geq 14$

$5 x + 10 y \leq 180, x \geq 10, y \geq 14$

Obviously $x \leq 10, y \leq 14$ and $5 x + 10 y \leq 180$

Type of questions	Time taken to solve	Mark s	Number of question
Short answered questions	5 minute	3	10
Long answered questions	10 minute	5	14

5x+10y≤180,x≤10,y≤14

x+10y≥180,x≤10,y≤14

5x+10y≥180,x≥10,y≥14

5x+10y≤180,x≥10,y≥14

Obviously x≤10,y≤14 and 5x+10y≤180

$5 x + 10 y \leq 180, x \leq 10, y \leq 14$

$x + 10 y \geq 180, x \leq 10, y \leq 14$

$5 x + 10 y \geq 180, x \geq 10, y \geq 14$

$5 x + 10 y \leq 180, x \geq 10, y \geq 14$

Obviously $x \leq 10, y \leq 14$ and $5 x + 10 y \leq 180$