A manufacturing firm produces tables and chairs with two machines lathe and grinder.

Available hours of each machine and their productivity per week are as follows:

Productivity $($unit processed per

hour$)$

Productivity $($unit processed per

hour$)$

Machine

Available

Hours

Table Chair

Lathe $1001012$

Grinder $501520$

Each table and chair costs $40$ and $25$ respectively. Sales potential for both items are

unlimited for their selling prices: $70/$unit for tables and $45/$unit for chairs. If we want to

maximise total profit and model it with a linear programming formulation for the decision

variables:

T: number of tables produced per week

C: number of chairs produced per week

What should be the constraints other than nonnegativity restrictions?

Select one:

a$.10$ T $+12$ C $<=100$

$15$ T $+20$ C $<=50$

b$.1/10$ T $+1/15$ C $<=100$

$1/12$ T $+1/20$ C $<=50$

c$.$ None of the others

d$.1/10$ T $+1/12$ C $<=100$

$1/15$ T $+1/20$ C $<=50$

e$.10$ T $+15$ C $>=100$

$12$ T $+20$ C $>=50$