Note: This is an open$-$book test. You must use Excel for Problem $1$ and use R for Problem $2.$

You can decide when to start working on the test and whether to take breaks but be sure to post

the deliverables in the ELMS before the end of Friday $5/10/2024.($Points will be deducted for

late submissions as per the Homework Submission Policy given in the course syllabus.$)$

Problems:

$(7$ points$)$ CC Chapter $12$ Problem $8($page $596)$ for Photon Technologies, Inc. to

determine optimal production plan.

Answer the following questions, NOT those given in the textbook, using Excel to solve

this linear optimization problem:

a$.$ Given the parameters in the problem, what would be the optimal production plan $($i$.$e$.,$

number of each of the three products at each of the two plants$)$ to meet the contracted

production quantity for each product $-$ at the minimum total cost $($of production and

transportation$)?$ What would be that minimum total cost?

b$.$ For that optimal production plan, what would be the unused capacity at each plant?

c$.$ If the company is able to reduce the unit cost of production for PT$-300$ at the

Philippines plant to $$1\mathrm{.}05,$ what would be optimal production plan? And what would

be the reduction of the total cost, if any?

$(7$ points$)$ CC Chapter $7$ problem $10($pages $359-360)$ on Resorts & Spas magazine

wanting to identify top beachfront boutique hotels based on ratings of their attributes; the

dataset "BeachFrontHotels" is provided; the ratings given in the dataset are on the scale

of $0$ to $100$ for each $-$ overall rating, comfort, amenities and in$-$house dining.

Answer the following questions, NOT the ones given in the textbook, by using R for

analysis:

a$.$ Develop all the seven linear regression models for the overall rating as the dependent

variable and the three independent variables $-$ comfort, amenities, and in$-$house

dining; and for each regression model, report if it is statistically significant $($at $0\mathrm{.}01$

level of significance$)$ and its goodness$-$of$-$fit $($r$-$square$).$

b$.$ Select a regression model from those seven developed in $($a$)$ as the best to estimate

the overall rating; explain your criteria for selection.

c$.$ What additional independent variable$($s$)$ should be considered for improved

goodness$-$of$-$fit? $[$Hint: think of attributes of such beachfront boutique hotels that

customers would normally seek for increased enjoyment and satisfaction from their

stay there.$]$