Edexcel D1 2023 January — Question 10

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2023
SessionJanuary
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear Programming
TypeGraphical optimization with objective line
DifficultyModerate -0.8 This is a standard linear programming question requiring graphing inequalities, identifying a feasible region, and using the objective line method. These are routine D1 techniques with no novel problem-solving required, making it easier than average but not trivial due to the multi-step nature and potential for arithmetic errors.
Spec7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables

10 x + 7 y & \leqslant 140
& x + y \leqslant 15
& 2 x + 3 y \geqslant 36
& x \geqslant 0 , \quad y \geqslant 0 \end{aligned} \end{array}$$ (c) Represent these constraints on Diagram 1 in the answer book. Hence determine, and label, the feasible region, \(R\).
(d) Use the objective line method to find the optimal number of each type of cake that Martin should make, and the amount of sugar used.
(e) Determine how much flour and how many eggs Martin will have left over after making the optimal number of cakes. BLANK PAGE \end{document}

10 x + 7 y & \leqslant 140 \\
& x + y \leqslant 15 \\
& 2 x + 3 y \geqslant 36 \\
& x \geqslant 0 , \quad y \geqslant 0
\end{aligned}
\end{array}$$

(c) Represent these constraints on Diagram 1 in the answer book. Hence determine, and label, the feasible region, $R$.\\
(d) Use the objective line method to find the optimal number of each type of cake that Martin should make, and the amount of sugar used.\\
(e) Determine how much flour and how many eggs Martin will have left over after making the optimal number of cakes.

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