The present paper is the result of a contemplative study of a multi-time control problem (MCP) by considering its associated NUTRI MULTI FOR WOMEN equivalent auxiliary control problem (MCP)$ _{ arsigma} $ via the exact $ l_{1} $ penalty method.Further study reveals that the solution set of the considered problem and the auxiliary problem exhibits an equivalence under the KT-pseudoinvexity hypothesis.Moreover, the PR783 study is extended towards the saddle point defined for (MCP) to establish the relationship between the solution set of multi-time control problem (MCP) and its associated equivalent auxiliary control problem (MCP)$ _{ arsigma} $.Finally, we present an illustrative application to authenticate the results presented in this paper.