Wilkinson Auto Dealership Sells Standard Automobiles and Station Wagons $\$ 250.00$

Essay

Wilkinson Auto Dealership sells standard automobiles and station wagons. The profit contribution for automobiles is $\$ 250.00$ per unit and $\$ 500.00$ per unit for station wagons. The company is planning the placement of orders with the manufacturer for next quarter. Orders for automobiles and station wagons can not exceed 320 and 160, respectively. Dealer preparation takes 2 hrs/auto and 5.0 hrs/wagon. They have 1100 hrs of preparation time next quarter. Autos take 1 unit of space, whereas wagons take 1.2 units of space. 480 units of space are available. In order to maintain some balance, the number of cars ordered should not be more than $150 \%$ the number of wagons ordered. Assume that they can sell all the autos and wagons they order for the quarter. The formulation of the problem is given below. Using excel-solver, completea sensitivity analysis of the objective function coefficients and report on the range of values of the coefficients that will leave the current solution optimal
find the range of feasibility for changes in the RHS of each constraint
Decision variables: Let $X_{1}$ be the number of automobiles and $X_{2}$ be the number of station wagons ordered next quarter.
Objective function: Max: $250 X_{1}+500 X_{2}$
Constraints: $X_{1} \leq 320 \quad X_{2} \leq 160 \quad 2 X_{1}+5 X_{2} \leq 1100 \quad 1 X_{1}+1.2 X_{2} \leq 480 \quad X_{1} \leq 1.5 X_{2}$
Variables are non-negative
Optimal solution using Solver: $X_{1}=206.25 \quad X_{2}=137.5$
The objective function value corresponding to the optimal solution is: $\$ 120.312 .50$