$4.$ Linear programming problem $(2\mathrm{.}5$ points$)$

Your answer should encompass the following aspects:

$1.$ Production Quantity for Maximum Profit: Determine the quantity of model H and model W that should be manufactured to achieve the highest profit $(0\mathrm{.}5$ points$)$

$2.$ Profit Projection: Determine the profit resulting from the optimal production mix $(0\mathrm{.}5$ points$)$

$3.$ Resource Utilization for Optimal Quantity: Provide details on the amount of fabrication and assembly required for manufacturing the optimal quantity. Extract this information from the second last column in the Excel sheet $(0\mathrm{.}5$ points$)$

$4.$ Constraint Slack Analysis: Evaluate the surplus capacity or slack available for each constraint. Derive this information from the difference between the last column and the second last column $(0\mathrm{.}5$ points$)$

$5.$ Excel Calculation Snapshot: Present a high$-$quality snapshot of the Excel calculations, ensuring inclusion in this document $(0\mathrm{.}5$ points$)$

Model H Model W Total Capacity

Number

Contribution $$40$ $$30$

Fabrication $42600$

Assembly $26480$