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

For the following shaded region,the linear constraints are:

Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $F = 4x + 6y$ be the objective function. The minimum value of $F$ occurs at $....$

The solution of the linear programming problem,maximize $Z = 3x_{1} + 5x_{2}$ subject to $3x_{1} + 2x_{2} \leq 18$,$x_{1} \leq 4$,$x_{2} \leq 6$,$x_{1} \geq 0$,$x_{2} \geq 0$ is:

For the following shaded area,the linear constraints except $x, y \geq 0$ are

The maximum value of $z=9x+11y$ subject to $3x+2y \leq 12$,$2x+3y \leq 12$,$x \geq 0$,$y \geq 0$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module