Max$|0\mathrm{.}40R+0\mathrm{.}60P,$

$s.t.$

Grade A crude oil available $0\mathrm{.}3R+0\mathrm{.}6P16800$

Production capacity $R+P50000$

Demand for premium $P20000$

$R,P0,$

$($b$)$ What is the optimal solution?

$R=$

$P=r$

profit $=$

$x$

$($c$)$ What is the value of the slack variable in the Grade A crude oil constraint?

Interpret this value.

After reaching the optimal solution, there is still this amount of grade A crude oil to be used.

After reaching the optimal solution, all available grade A crude oil has been used.

O In order to reach the optimal solution, this amount of grade A crude oil is required.

What is the value of the slack variable in the Production capacity constraint?

Interpret this value.

After reaching the optimal solution, the refinery is still able to produce this amount of gasoline.

After reaching the optimal solution, the total production capacity is used.

In order to reach the optimal solution, the refinery must produce this amount of additional gasoline.

What is the value of the slack variable in the Demand for premium constraint?

Interpret this value.

After reaching the optimal solution, the produced amount of premium gasoline is this much less than the maximum demand.

After reaching the optimal solution, the maximum demand for premium gasoline has been reached.

In order to reach the optimal solution, this amount of additional premium gasoline needs to be produced in order to meet demand.

$($d$)$ What are the binding constraints? $($Select all that apply.$)$

$$ grade A crude oil available

demand for premium

production capacity