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IAL 2025 Jan D1 Q8

A Level / Edexcel / D1

IAL 2025 Jan Paper · Question 8

题目

Problem

Figure 4 shows the constraints of a linear programming problem in xx and yy.

The unshaded area, including its boundaries, forms the feasible region RR.

An objective line has been drawn and labelled on the graph.

(a) State the four inequalities that define the feasible region.

(2)

The maximum value of the objective function is 6289\dfrac{628}{9}.

The minimum value of the objective function is 2607\dfrac{260}{7}.

(b) Determine the objective function, showing your working clearly.

(5)

The practical solution to the linear programming problem requires integer values.

(c) State the minimum integer solution for this problem.

(1)
题目中文翻译

图 4 显示了 xxyy 的线性规划问题的约束条件。

未阴影区域(包括其边界)构成可行域 RR

图上已画出并标注了一条目标线。

(a) 写出定义可行域的四个不等式。

目标函数的最大值为 6289\dfrac{628}{9}

目标函数的最小值为 2607\dfrac{260}{7}

(b) 确定目标函数,清楚展示运算过程。

该线性规划问题的实际解需要整数值。

(c) 说明此问题的最小整数解。

解答