Mathematics

Linear Programming

Grade 12 · High School

Answer every question first, then press Finish to see your score and explanations.

Question 1 of 20Easy
The value of $2 x + 3 y$ for $x = 1$ and $y = 2$ is ...
Question 2 of 20Easy
A point satisfying the inequality $x + y \leq 5$ is ...
Question 3 of 20Easy
The constraint "at least 8" for the variable $x$ is written as ...
Question 4 of 20Easy
The feasible region $x \geq 0$ and $y \geq 0$ lies in quadrant ...
Question 5 of 20Easy
The optimum value of a linear program is attained at ...
Question 6 of 20Easy
The maximum of $f = 2 x + y$ at the vertices $(0, 0)$ , $(4, 0)$ , and $(0, 3)$ is ...
Question 7 of 20Medium
The maximum of $f = 3 x + 2 y$ subject to $x \geq 0$ , $y \geq 0$ , and $x + y \leq 4$ is ...
Question 8 of 20Medium
The maximum of $f = x + y$ subject to $x + 2 y \leq 6$ , $2 x + y \leq 6$ , $x \geq 0$ , $y \geq 0$ is ...
Question 9 of 20Medium
The minimum of $f = 2 x + 3 y$ subject to $x + y \geq 4$ , $x \geq 0$ , $y \geq 0$ is ...
Question 10 of 20Medium
The maximum of $f = 5 x + 4 y$ subject to $x + y \leq 5$ , $x \geq 0$ , $y \geq 0$ is ...
Question 11 of 20Medium
A tailor makes two dress models. Model A needs 1 m of cloth and model B needs 2 m. There are 10 m available. If $x$ is the number of model A and $y$ of model B, the cloth constraint is ...
Question 12 of 20Medium
The maximum of $f = 4 x + 3 y$ subject to $x + y \leq 6$ , $x \geq 0$ , $y \geq 0$ is ...
Question 13 of 20Medium
The vertices of the feasible region $x + y \leq 4$ , $x \geq 0$ , $y \geq 0$ are ...
Question 14 of 20Medium
A business makes two products. Product A earns Rp2,000 per unit and product B Rp3,000 per unit. Output is limited by $x + y \leq 100$ and $x \leq 60$ . The maximum profit is ...
Question 15 of 20Hard
The maximum of $f = 3 x + 5 y$ subject to $x + 2 y \leq 8$ , $3 x + 2 y \leq 12$ , $x \geq 0$ , $y \geq 0$ is ...
Question 16 of 20Hard
The minimum of $f = 3 x + 4 y$ subject to $2 x + y \geq 6$ , $x + 2 y \geq 6$ , $x \geq 0$ , $y \geq 0$ is ...
Question 17 of 20Hard
A factory makes chairs ( $x$ ) and tables ( $y$ ). A chair needs 2 wood units and 1 work hour; a table needs 1 wood unit and 2 work hours. There are 24 wood units and 24 work hours. Chair profit is Rp50,000 and table Rp60,000. The maximum profit is ...
Question 18 of 20Hard
The maximum of $f = 2 x + 3 y$ subject to $x + y \leq 10$ , $x + 2 y \leq 16$ , $x \geq 0$ , $y \geq 0$ is ...
Question 19 of 20Hard
The minimum of $f = x + y$ subject to $2 x + y \geq 8$ , $x + 2 y \geq 8$ , $x \geq 0$ , $y \geq 0$ is ...
Question 20 of 20Hard
A factory makes product I ( $x$ ) needing 3 work hours and product II ( $y$ ) needing 2 work hours. There are 60 work hours and demand for product I is at most 10 units. Product I profit is Rp20,000 and product II Rp15,000. The maximum profit is ...

0/20 answered