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Edexcel A-Level Mathematics AS D1.5.3 Consideration of Problems Where Solutions Must Have Integer Questions

Practise integer linear-programming decisions by checking whole-number feasible points against constraints and the problem context.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • Choose whole-number candidates from the feasible region when variables count items or orders.
  • Check integer points against every constraint before stating the final quantity or total.

Edexcel A-Level Mathematics AS D1.5.3 Consideration of Problems Where Solutions Must Have Integer Questions question 1

[Maximum number: 5]

The head of a Mathematics department needs to order three types of paper. The three types of paper are plain, lined and graph.

All three types of paper are sold in reams. (A ream is 500 sheets of paper.)
Based on the last academic year the head of department formed the following constraints.
- At least half the paper must be lined
- No more than 15% of the paper must be graph paper
- The ratio of plain paper to graph paper must be 5: 2

The cost of each ream of plain, lined and graph paper is £ 5, £ 12 and £ 15 respectively. The head of department has at most £ 834 to spend on paper.

The head of department wants to maximise the total number of reams of paper ordered.
Let x, y and z represent the number of reams of plain paper, lined paper and graph paper ordered respectively.

Question (a)

(a)

Determine

[ 5 ]

Question (i)

(i)

the total number of reams of paper to be ordered,

[ 2 ]

Question (ii)

(ii)

the number of reams of graph paper to be ordered.

[ 3 ]
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