a$)$ Using a computer software for solving LP$,$ the optimal solution achieved is:

$x_1=7\mathrm{.}95($round your response to two decimal places$).$

$x_2=5\mathrm{.}95($round your response to two decimal places$).$

$x_3=12\mathrm{.}59($round your response to two decimal places$).$

Contribution $($objective value$)=$

$($round your response to two decimal places$).$

b$)$ Machine $1$ has $0$ hours of unused time available at the optimal solution $($round your response to two decimal places$).$

Machine $2$ has hours of unused time available at the optimal solution $($round your response to two decimal places$).$

Machine $3$ has $0$ hours of unused time available at the optimal solution $($round your response to two decimal places$).$

c$)$ An additional hour of time available for third machine, is worth dollars to the firm $($round your response to two decimal places$).$