**7. Numerical Illustrations**

Here, we have discussed validation of the proposed work. During the validation process, two numerical examples of a hypothetical system are considered as follows:

**Example 1:** In this numerical example, the hypothetical data of input parameters are taken in the following way:

*A* = 690, *B* = 700, *α* = 325, *β* = 690, *γ* = 365, *δ* = 325, *θ*<sup>1</sup> = 0.22, *η* = 0.9, *k* = 0.2, *a* = 150, *b* = 0.5, *Co* = 450, *cp* = 50, *h* = 0.5.

> **Example 2:** Here, the values of preservation parameters are taken as *m* = 0.7 and the other input parameters are taken to be the same as Example 1.

> Example 1 and Example 2 are solved by DE and SA, which are codded in Mathematica software, and the obtained results are displayed in Tables 4 and 5, respectively. Moreover, to show the concavity of the objective function, the pictorial representations of the average profit function versus independent variables taken two at a time w.r.t. Example 2 are depicted in Figures 4–6.




**Table 5.** Best-found solution of Example 2.

*Discussion*

From the solution of Examples 1 and 2 (cf. Tables 2 and 3), the following findings are observed.


**Figure 4.** Profit function with respect to *t*<sup>1</sup> and *p*.

**Figure 5.** Profit function with respect to *t*<sup>1</sup> and *ξ*.

**Figure 6.** Profit function with respect to *ξ* and *p*.
