<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN"
  "https://jats.nlm.nih.gov/publishing/1.2/JATS-journalpublishing1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink"
         xmlns:mml="http://www.w3.org/1998/Math/MathML"
         article-type="research-article"
         dtd-version="1.2">

  <!-- ============================================================ FRONT -->
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">IJLTEMAS</journal-id>
      <journal-title-group>
        <journal-title>International Journal of Latest Technology in Engineering, Management &amp; Applied Science (IJLTEMAS)</journal-title>
        <abbrev-journal-title abbrev-type="publisher">IJLTEMAS</abbrev-journal-title>
      </journal-title-group>
      <issn pub-type="epub">2278-2540</issn>
      <publisher>
        <publisher-name>IJLTEMAS</publisher-name>
      </publisher>
    </journal-meta>

    <article-meta>
      <!-- IDs -->
      <article-id pub-id-type="publisher-id">288</article-id>
            <article-id pub-id-type="doi">10.51583/IJLTEMAS.2026.150800094</article-id>
      
      <!-- Categories -->
            <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Education</subject>
        </subj-group>
      </article-categories>
      
      <!-- Title -->
      <title-group>
        <article-title>A Critical Review of the Application of the Simplex Method on Profit Maximization in Baker’s Cottage</article-title>
      </title-group>

      <!-- Authors -->
      <contrib-group>
                <contrib contrib-type="author">
                    <name>
            <surname>Patrick Enyi</surname>
            <given-names>Enyi</given-names>
          </name>
                              <aff>
            Department of Accounting, Babcock University, Ilishan-Remo, Nigeria                        <country>Nigeria</country>
                      </aff>
                    
        </contrib>
              </contrib-group>

      <!-- Volume / Issue / Pages -->
            <volume>15</volume>
                  <issue>8</issue>
                        <fpage>1293</fpage>
            <lpage>1302</lpage>
            
      <!-- Dates -->
      <history>
                <date date-type="received">
          <day>30</day>
          <month>08</month>
          <year>2026</year>
        </date>
                        <date date-type="accepted">
          <day>04</day>
          <month>09</month>
          <year>2026</year>
        </date>
              </history>

            <pub-date pub-type="epub">
        <day>18</day>
        <month>09</month>
        <year>2026</year>
      </pub-date>
      
      <!-- DOI Self-URI -->
            <self-uri xlink:href="https://doi.org/10.51583/IJLTEMAS.2026.150800094"/>
      
      <!-- Keywords -->
            <kwd-group kwd-group-type="author">
                <kwd>Linear programming; simplex method; profit maximization; Baker’s Cottage; slack variables; resource allocation; Excel Solver; optimality.</kwd>
              </kwd-group>
      
    </article-meta>
  </front>

  <!-- ============================================================ BODY (Abstract) -->
  <body>
        <sec>
      <title>Abstract</title>
      <p>This review critically examines the application of the simplex method for profit maximization in Baker’s Cottage as reported by Azman et al. (2022). The reviewed study formulated a linear programming model involving five bakery products and seven production resources and used Microsoft Excel Solver to identify a profit-maximizing product mix with a reported monthly profit of RM40,270.42. Although the study provides a useful practical demonstration of linear programming in production planning, this review identifies important analytical and interpretive limitations. In particular, the reported solution was presented as optimal without sufficient intermediate simplex information, such as a final simplex tableau or reduced-cost analysis, to permit independent verification. An independent simplex solution using ValuStats (VSP) 2.0 confirms the reported maximum profit and resource-slack values but reveals that the optimal allocation involves Chicken Floss, Spicy Floss and Frank Cheese rather than only Chicken Floss and Frank Cheese as emphasized in the original article. The review further demonstrates that water and sugar are the binding constraints, while flour, yeast, egg, milk and butter have substantial unused capacities. A supplementary case study illustrates how slack-variable values can provide additional information for resource-allocation and managerial decisions. The review concludes that simplex-based analysis should extend beyond the identification of an optimal objective value to include explicit optimality verification and meaningful interpretation of binding and non-binding constraints. Such an approach enhances the reproducibility, managerial relevance and decision-support value of linear programming applications.</p>
    </sec>
      </body>

  <!-- ============================================================ BACK (References) -->
    <back>
    <ref-list>
      <title>References</title>
            <ref id="ref1">
        <label>1</label>
        <mixed-citation>Anieting, A. E., Ezugwu, V. O., &amp; Ologun, S. (2013). Application of linear programming technique in the determination of optimum production capacity. IOSR Journal of Mathematics, 5(6), 60–65. https://doi.org/10.9790/5728-0566265⁠�</mixed-citation>
      </ref>
            <ref id="ref2">
        <label>2</label>
        <mixed-citation>Azman, N. Z. M., Mohamed, N. A., Mohamed, N. F., &amp; Musa, M. (2022). Application of the simplex method on profit maximization in Baker’s Cottage. Indonesian Journal of Electrical Engineering and Computer Science, 27(2), 1034–1042. https://doi.org/10.11591/ijeecs.v27.i2.pp1034-1042⁠�</mixed-citation>
      </ref>
            <ref id="ref3">
        <label>3</label>
        <mixed-citation>Enyi, P. E. (2012). The sub-optimal effect of the simplex solution method in resource allocation using the linear programming model. American International Journal of Contemporary Research, 2(8), 185–193.</mixed-citation>
      </ref>
            <ref id="ref4">
        <label>4</label>
        <mixed-citation>Keyeke, G. C. (2006). Operations research. QAT Publishers.</mixed-citation>
      </ref>
            <ref id="ref5">
        <label>5</label>
        <mixed-citation>Levin, R. I., Kirkpatrick, C. A., &amp; Rubin, D. S. (2005). Quantitative approaches to management. McGraw-Hill.</mixed-citation>
      </ref>
            <ref id="ref6">
        <label>6</label>
        <mixed-citation>Mohan, L. (2018). Application of linear programming for optimal use of raw materials in bakery. Research Review International Journal of Multidisciplinary, 3(11), 1168–1172.</mixed-citation>
      </ref>
            <ref id="ref7">
        <label>7</label>
        <mixed-citation>Oladejo, N. K., Abolarinwa, A., &amp; Salawu, S. O. (2020). Linear programming and its application techniques in optimizing portfolio selection of a firm. Journal of Applied Mathematics, 2020, Article 8817909. https://doi.org/10.1155/2020/8817909⁠�</mixed-citation>
      </ref>
            <ref id="ref8">
        <label>8</label>
        <mixed-citation>Pan, P.-Q. (2025). Face method: Toward the new generation of linear programming. Springer. https://doi.org/10.1007/978-3-031-93594-7⁠�</mixed-citation>
      </ref>
            <ref id="ref9">
        <label>9</label>
        <mixed-citation>Shakirullah, F. M., Ahammad, M. U., &amp; Uddin, M. F. (2020). Profit optimization of an apparel industry in Bangladesh by linear programming model. American Journal of Applied Mathematics, 8(4), 182–189. https://doi.org/10.11648/j.ajam.20200804.13⁠�</mixed-citation>
      </ref>
            <ref id="ref10">
        <label>10</label>
        <mixed-citation>Sogunro, A., &amp; Adekanye, F. (2009). Linear programming for business, banking and finance. F &amp; A Publishers.</mixed-citation>
      </ref>
            <ref id="ref11">
        <label>11</label>
        <mixed-citation>Stafford, L. W. T. (1981). Business mathematics (2nd ed.). Macdonald and Evans.</mixed-citation>
      </ref>
            <ref id="ref12">
        <label>12</label>
        <mixed-citation>Tripathi, S. K., &amp; Kumar, R. (2023). A short literature on linear programming problem. EAI Endorsed Transactions on Energy Web, 10. https://doi.org/10.4108/ew.4516⁠�</mixed-citation>
      </ref>
            <ref id="ref13">
        <label>13</label>
        <mixed-citation>Wolde, B. C., &amp; Larsson, T. (2024). A steepest feasible direction method for linear programming: Derivation and embedding in the simplex method. Operations Research and Decisions, 34(2), 163–182. https://doi.org/10.37190/ord2402010⁠�</mixed-citation>
      </ref>
          </ref-list>
  </back>
  
</article>
