Venus Robotics has two employee training programs $-$ Teamwork and Creative Thinking. The

training programs are delivered to $20$ employees at a time. Teamwork training is a $3$ day program

and costs $$10,000$ per offering; Creative Thinking lasts $2$ days and costs $$8,000.$ Venus Robotics'

management has decided that at least $15$ training programs should be offered total, with at least $6$

of these on Teamwork and at least $6$ on Creative Thinking. However, they do not wish their

employees to use more than $1000$ days of training. $($One Teamwork training program occupies $20$

employees for $3$ days, so requires $60$ days of training time.$)$

$6)$ Manually calculate the range of values for the cost of Teamwork training for which the

current basis remains optimal.

$7)$ Manually calculate the range of values for the cost of Creative Thinking training for which

the current basis remains optimal.

$8)$ Manually calculate the range of values for the number of training programs for which the

current basis remains optimal.

$9)$ Manually calculate the range of values for the number of training days for which the current

basis remains optimal.

$10)$ Manually calculate the range of values for the number of Teamwork training programs for

which the current basis remains optimal. $.$

$11)$ Manually calculate the range of values for the number of Creative Thinking training

programs for which the current basis remains optima