#$1$

To crosstrain its data scientists on multiple programming techniques, DataVista plans to offer

a three$-$day workshop on R and a four$-$day workshop on Python. The chief data scientist has

requested that at least four of each type of workshop be offered during the current quarter. The

consultant that provides these workshops has $36$ days available during this quarter, and DataVista

must contract with them for at least $10$ workshops. The cost to DataVista is $$400$ for each R

workshop and $$300$ for each Python workshop.

Formulate a linear programming model that can be used to determine the cost$-$minimizing number

of each type of workshop to offer this quarter. Solve the LP using the graphical solution method:

draw and label all constraints, identify the feasible region, draw a representative objective function,

identify the optimal solution, and indicate the optimal objective function value. Provide all

constraints in standard form.

#$2$

Consider the following linear programming model with two decision variables, $x_1$ and $x_2.$

$ma{?}_1+2x_2$

$s.t.$

$2x_1+3x_{2}90$

$2x_1+x_{2}50$

$x_{1}10$

$x_{2}20$

$x_1,x_{2}0$

Use the graphical solution method to determine the optimal solution to this linear programming

model. Include all components as requested in Question #$1.$