A toy company manufactures two types of dolls | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $x$ and $y$ be the number of dolls of type $A$ and $B$ respectively that are produced per week.The given problem can be formulated as follows:

Vedclass · Accepted Answer

$800$ dolls of type $A$ and $400$ dolls of type $B$

Vedclass · Answer

(A) Let $x$ and $y$ be the number of dolls of type $A$ and $B$ respectively that are produced per week.The given problem can be formulated as follows:Maximize $z = 12x + 16y$ .....$(1)$Subject to the constraints:$x + y \leq 1200$ .....$(2)$$y \leq \frac{x}{2} \Rightarrow x \geq 2y$ .....$(3)$$x - 3y \leq 600$ .....$(4)$$x, y \geq 0$ .....$(5)$The feasible region is determined by the system of constraints. The corner points of the feasible region are $O(0,0)$,$A(600,0)$,$B(1050,150)$,and $C(800,400)$.The values of $z$ at these corner points are as follows:      Corner point    $z = 12x + 16y$        $O(0,0)$    $0$        $A(600,0)$    $7200$        $B(1050,150)$    $12(1050) + 16(150) = 12600 + 2400 = 15000$        $C(800,400)$    $12(800) + 16(400) = 9600 + 6400 = 16000$  The maximum value of $z$ is $16000$ at $(800, 400)$.Thus,$800$ dolls of type $A$ and $400$ dolls of type $B$ should be produced weekly to maximize the profit.

Similar Questions

The shaded area in the figure below is the solution set for a certain linear programming problem. Then the linear constraints are given by:

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ subject to the constraints $x + 3y \leqslant 60$,$x + y \geqslant 10$,$x - y = 0$,and $x, y \geqslant 0$ is:

For the linear programming problem, $x + 2y \leq 10$, $3x + y \leq 12$, $x, y \geq 0$, the maximum value of $z = 5x + 10y$ occurs at every point on the line segment joining the points..

If the feasible region is as shown in the figure,then the related inequalities are:

The feasible region for the constraints $x-2 \leqslant y$,$x \geqslant y-1$,$x \geqslant 2$,$y \leqslant 4$,$x, y \geqslant 0$ is represented by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module