The following assignment is a group assignment. Only ONE attempt is permitted for each group.

Turlock Auto, a car dealership, is planning for the upcoming spring sale season. The dealership is offering three types of vehikles, sedan, SUV and pickup truck. The dealership has $5,000$ sqft parking space availabic for displaying all its inventory and has $$981,000$ budget for purchasing new car tiventory from a car manufacturer. The purchasing cost and required parking space for each type of wehicle is listed in the table below. It is estimated that the maximum possible demand for sedan, SUV and truck are $16,22$ and $12$ during this sale season. For each sold sedan, SUV and truck, the dealer will make an average profit of $$1,000,$$$1,200$ and $$1400$ respectively. The dealership wants to decide how many sedan, SUV and truck it should purchase and display in its parking lot to make the most profit.

Formulate this problem as a linear programming model and solve the formulated model using both Excel and POM$-$QM$.$ Note: type your model formulation $($including decision variables, objective function and all constraints$)$ into the text entry provided and then upload your completed excel and POM$-$QM files.

$\backslash$table$[[$Types of vehicles,Sedan,SUV,Truck$],[$Cost $($$$/$car$),20,000,25,000,28,000],[$Parking space $($sqft$/$car$),100,110,130]]$