A company manufactures two varieties of pens: $A$ and $B$. Each pen $A$ needs $2$ hours of labor, whereas each pen $B$ needs $1$ hour of labor. Total labor hours available is $500$ hours per month. The demand for $A$ pens is $\rm{Rs.}150$ per month. The demand for $B$ pens is $\rm{Rs.}250$ per month. The profits that the two varieties fetch are $\rm{Rs.}8$ and $\rm{Rs.}5$ per pen. Formulate the linear program.
Can somebody tell me how to solve this problem?
The problem can be solved with any software or algorithm for (linear) integer optimization problems (since you don't want to manufacture fractions of pens). The free software R features some optimization packages for your type of problem such as the
lpSolvepackage. Commerical solvers like Cplex or Xpress will also easily solve your problem and find the optimal solution.