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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