Note: This Problem Requires the Use of a Linear Programming $$y _ { i } = \left\{ \begin{array} { l } 1 , \text { if product } j \text { is produced } \\0 , \text { otherwise }\end{array} \right.$$

question 21

Multiple Choice

Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies) . The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example) :
Max 10x1 + 12x2 - 100y1 - 200y2
s.t. 5x1 + 10x2 ? 1000 {Constraint 1}
2x1 + 5x2 ? 2500 {Constraint 2}
2x1 + 1x2 ? 300 {Constraint 3}
My1 ? x1 {Constraint 4}
My2 ? x2 {Constraint 5} $$y _ { i } = \left\{ \begin{array} { l } 1 , \text { if product } j \text { is produced } \\0 , \text { otherwise }\end{array} \right.$$
Set up the problem in Excel and find the optimal solution. What is the optimal production schedule?

• A) 133? cakes, 33? pies
• B) 133? cakes, 0 pies
• C) 0 cakes, 33? pies
• D) 33? cakes, 133? pies
• E) 133? cakes, 133? pies

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Definitions:

Maintenance Margin

The minimum account balance that an investor must maintain in a margin account after buying securities on credit, to protect brokers against deficits.

Private Placements

The sale of stocks, bonds, or securities directly to private investors rather than through a public offering in the capital markets.

Primary Security Offerings

The process by which new securities are issued and sold to investors, allowing companies or governments to raise capital.

Institutional Investors

Entities such as banks, insurance companies, and pension funds that invest large sums of money into financial markets.