$4-22$:

Please answer the below questions in regards to the Good$-$to$-$Go Business:

$($a$)$ What is the optimal production plan? Which of the resources are scarce?

$($b$)$ Suppose Good$-$to$-$Go is considering including a polishing process, the cost of which would be added directly to the price. Each Standard suitcase would require $10$ minutes of time in this treatment, each Deluxe suitcase would need $15$ minutes, and each Luxury suitcase would need $20$ minutes. Would the current production plan change as a result of this additional process if $170$ hours of polishing time were available? Explain your answer.

$($c$)$ Now consider the addition of a waterproofing process where each Standard suitcase would use $1$ hour of time in the process, each Deluxe suitcase would need $1\mathrm{.}5$ hours, and each Luxury suitcase would require $1\mathrm{.}75$ Exercises $229$ hours. Would this change the production plan if $900$ hours were available? Why or why not?

Please answer all questions and show work thank you