The Go-to-Go Suitcase Company linear programming model has all the objective function coefficients known with certainty. Primarily, changes in the objective function coefficients (OFCs) of a product changes the slope level of the level curve. In turn, changes in the slope of the level curve result in a change in the optimal solution of the function. The objective of the firm is to maximize profit. Therefore, $7668.00 is the optimal solution of the objective function.
The objective coefficient for the standard products is 10. However, the standard products have an allowable increase of 3.50 and a 2.56 allowable decrease. Therefore, a 10 unit increase in the standard products sold would not affect the optimal solution. On the other hand, a unit change of more than ten units in the number of standard units sold would change the level curve resulting in a change in the optimal solution. Similarly, a 2.56 unit decrease in the standard products would not affect the optimal solution. However, a more than 2.56 units decrease would change the location of the optimal solution provided the other objective coefficients remain constant. Similarly, changes above the allowable decrease and increase of luxury and deluxe products result in a change in the optimal solution provided the other objective coefficients remain constant.
However, if the products’ selling prices per unit cannot be changed, one can still increase the objective function coefficients within their allowable increase. The increase in the OFCs is achieved by changing the Right Hand Side (RHS) value of a constraint. Shadow prices indicate the changes in the objective function value resulting from a unit change in the RHS value of the constraint give that all the other coefficients are held constant. However, the shadow prices hold only if the changes remain in the allowable increase. Furthermore, the changes in the RHS of a binding constraint result in significant changes in the optimal solution as well as in the feasible region. However, all of these changes are as a result of the change in the OFCs caused by changes in the shadow prices. For instance, a unit increase in the RHS of cutting and coloring would increase the shadow price by 4.38 units resulting in changes in the OFCs within the allowable increase.
Changes in resource availability affect material costs per unit. A decrease in the availability of the resources decreases the material cost per unit. On the other hand, a decline in resource availability increases the material unit cost. Material cost is a component of the objective function. Therefore, a unit change in the unit cost of the materials affects the optimal solution. For instance, a unit increase in the material cost of standard products resulting from scarcity of resources raises the price from $6.25 to $7.25. The unit increase in material cost reduces the unit cost hence cutting the total profit which is the optimal solution. Similarly, a decrease in the availability of labor increases the labor costs reducing the benefits. Therefore, a reduction in the availability of resources decreases the profit of the Go-to-Go Suitcase Company. On the other hand, an increase in the availability of resources increases the company’s optimal solution.
In summary, changes in the OFCs of the products, as well as the availability of resources, affect the optimal solution of the company. Changes in the OFCs within the allowable increase and decrease do not affect the optimal solution. However, changes above the allowable increase and decrease shift the location of the optimal solution. Moreover, changes in the availability of resources such as labor and materials change the profit levels of the firm.
Greco, S., Figueira, J., & Ehrgott, M. (2016). Multiple criteria decision analysis. New York: Springer.
Vanderbei, R. J. (2015). Linear programming. Heidelberg: Springer.