Problem $1$: Gear Up wants to maximize their profits by determining the optimal production quantities for their two most popular backpacks: The $($H$)$ and the Climber $($C$).$

Data:

Profit per backpack: Hiker is $$40/$bag and Climber is $$50/$bag

Production time per backpack $($hours$)$: Hiker is $2$ hours$/$bag and Climber is $3$ hour$/$bag

Available production hours per week: $120$ hours

Constraints:

$1.$ Gear Up has limited sewing machine capacity. They can't exceed the total available production hours.

$2.$ There's also a limitation on fabric availability. Each Hiker backpack uses $3$ yards of fabric, while each Climber backpack uses $4$ yard

s$.$ Gear Up has $240$ yards of fabric available per week.

: Solve the Optimization Problem

Question $4(25$ points$)$: On a piece of paper, please use the graphical method we learned in class to identify the feasible region. After you create the graph and label the Feasible Region, please take a picture of your graph, and insert the picture to this word document.

Question $5(5$ points$)$: Based on the graph you developed in question $4,$ what is the optimal number of Hiker backpacks and Climber backpacks Gear Up should produce to maximize their total weekly profit?

Question $6(5$ points$)$: Based on the graph you developed in question $4,$ what is the highest total weekly profit Gear Up can achieve?

Question $7(25$ points$)$: Open a blank Excel file and enter the data information you needed to solve this linear problem on Excel. Apply Excel Solver function to solve this problem. Please take a screenshot of your Excel Solver solution and insert the screenshot to this word document.

Question $8(5$ points$)$: Based on the excel output in question $7,$ what is the optimal number of Hiker backpacks and Climber backpacks Gear Up should produce to maximize their total weekly profit?

Question $9(5$ points$)$: Based on the excel output in question $7,$ what is the highest total weekly profit Gear Up can achieve?