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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/18h/d/solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 18H / d / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

The dual is

maximize e^{T} y subject to A y \leq e, y \geq 0,

(1)

which is in standard maximization form after adding nonnegative slack variables. The simplex pivots first introduce the variable with coefficient seven and then the remaining payoff column; the optimum occurs where both constraints bind:

y_{1} + 5 y_{2} = 1, 7 y_{1} + 3 y_{2} = 1.

(2)

Thus

y = (1/16, 3/16)

and the dual value is

1/4

. Complementary slackness gives

x = (1/8, 1/8)

. Hence

v = 4

and the normalized optimal strategies are

p = (1/2, 1/2), q = (1/4, 3/4), v = 4 .

(3)

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