Introduction
Business organizations or firms, which seek to use the technique of analysis in order to understand complex mathematical together with other statistical measurements in research, uses quantitative analysis method. They do this by assigning numerical values or variables as the analysts try in quantitatively replicating the mathematics into reality. It is performed for many reasons like to know the performance, evaluate, and value in terms of financial instruments the correct values that can be used in the objective function. In the market structure, this technique is used to reflect or show changes according to price and the nature of variation.
in the light of the above discussion, the question handled below is set o solve a graphical models to enable managers to visualize the objective function as well as the constraints which shall be used to give feasible solutions so that the manager can make informed decisions. The information is given on the company A will be applied to determine the quantities of the pet foods that are produced in different brands X and Y.
Discussion
The initiative in this research is to come up with a correct objective function. In addition, it will be necessary to come up with the right constraints of the model and then state them in a mathematical way. These constraints are the ones to be solved in the objective function to get the results, which will be used by the managers to make informed decisions. In the model above, the objective function can be formulated based on the values given as follows:
Constraints
- X+2Y≥500
- 2X+Y≥150
- 6X+Y≤400
- 10X+Y≤300
- Φ=100X+12.5Y
The first two constraints are maximization since they do not specify the maximum quantities to be plotted. Any value beyond the ones indicated is still acceptable. The other two are minimization problems as they show the minimum values, beyond which the constraints will not be acceptable. The last function number (5) is the objective function of the equations to be solved by the model.
The possible values of X and Y will be (0,150), (10,135), (15,100), and (18, 50). From the calculations in the objective function, (15,100) gives the highest values of the products, thus X=15 units while Y=100. The feasible region was obtained when plotting the graphs and shading the unwanted regions. The remaining region that was never shaded is the feasible solution, in this case the region below the color line and the profit function.
Based on the above results, the total profit contribution will be calculated as shown below Φ=100X+12.5Y= Φ=100*15+12.5*100= 2750 Units
