Maharashtra Board Solutions for Chapter: Linear Programming, Exercise 5: Miscellaneous Exercise

Solve each of the following L.P.P.

Maximize $z=2x+3y$ subject to $x-y\ge 3,x\ge 0,y\ge 0$

Solve each of the following L.P.P.

Maximize $z=4x_1+3x_2$ subject to $3x_1+x_2\le 15,3x_1+4x_2\le 24,x_1\ge 0,x_2\ge 0$

Solve each of the following L.P.P.

Maximize $z=60x+50y$ subject to $x+2y\le 40,3x+2y\le 60,x\ge 0,y\ge 0$

Solve each of the following L.P.P.

Maximize $z=4x+2y$ subject to $3x+y\ge 27,x+y\ge 21,x+2y\ge 30;\mathrm{x}\ge 0,\mathrm{y}\ge 0$

A carpenter makes chairs and tables. Profits are $\mathrm{Rs}.140/-$ per chair and $\mathrm{Rs}.210/-$ per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by following table:

Formulate the above problem as L.P.P. Solve it graphically to get maximum profit.

A chemical company produces a chemical containing three basic elements $A,B,C$ so that it has at least $16$ liters of $A,24$ liters of $B$ and $18$ liters of $C$. This chemical is made by mixing two compounds $\mathrm{I}$ and $\mathrm{II}$. Each unit of compound $\mathrm{I}$ has $4$ liters of $A,12$ liters of $B,2$ liters of $C$. Each unit of compound $\mathrm{II}$ has $2$ liters of $A,2$ liters of $B$ and $6$ liters of $C$. The cost per unit of compound $\mathrm{I}$ is $\mathrm{Rs}.800/-$ and that of compound $\mathrm{II}$ is $\mathrm{Rs}.640/-$. Formulate the problem as L.P.P. and solve it to minimize the cost.

A firm manufactures two prođucts $A$ and $B$ on which profit earned per unit $\mathrm{Rs}.3/-$ and $\mathrm{Rs}.4/-$ respectively. Each product is processed on two machines $M_1$ and $M_2$. The product A requires one minute of processing time on $M_1$ and two minute of processing time on $M_2,B$ requires one minute of processing time on $M_1$ and one minute of processing time on $M_2$. Machine $M_1$ is available for use for $450$ minutes while $M_2$ is available for $600$ minutes during any working day. Find the number of units of product $A$ and $B$ to be manufactured to get the maximum profit.

A firm manufacturing two types of electrical items $A$ and $B$, can make a profit of $\mathrm{Rs}.20 /-$ per unit of $A$ and $\mathrm{Rs}.30/-$ per unit of $B$. Both $A$ and $B$ make use of two essential components a motor and a transformer. Each unit of A requires $3$ motors and $2$ transformers and each units of $B$ requires $2$ motors and $4$ transformers. The total supply of components per month is restricted to $210$ motors and $300$ transformers. How many units of $A$ and $B$ should the manufacture per month to maximize profit? How much is the maximum profit?