Edexcel IAL Mathematics D1.5 linear programming

$$\frac12(x+y+z)\le y \quad(\Rightarrow x-y+z\le0)$$
M1
$$\frac3{20}(x+y+z)\ge z \quad(\Rightarrow 3x+3y-17z\ge0)$$
M1
2x=5z
B1
$$5x+12y+15z\le834$$
B1

Eliminating z from the objective x+y+z and at least one correct constraint, or stating the objective and eliminating z from at least two correct constraints.
M1

Maximise P=1.4x+y, subject to
$$\begin{aligned} 11x+12y&\le834\\ 7x-5y&\le0\\ 19x-15y&\le0\\ x&\ge0,\quad y\ge0 \end{aligned}$$
A1 A1
(7)

B 1

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B1ft.Wordyrees
B1

B1ft

B1

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Total weight of the MST is therefore 14 x+5 y-4

A1

14 x+5 y-4=73 and testing integer value points inside FR

M1dep

x=3 and y=7

A1

15 marks

Notes for Question 7

a1M1: Explaining that if CD is not in the tree than AD must be e.g. 'the MST must contain D so if CD is not in the tree then AD is'. Must explicitly mention arc AD for this mark, so as a minimum accept, 'AD must be in the MST'

a1A1: Correct reasoning and derivation of the given result ( $2 y+x>3 y-7 \Rightarrow y<x+7$ ) - as the answer is given we must see at least 2 y+x>3 y-7 or 3 y-7<2 y+x before the required answer

SC (Special Case) in (a): $2 y+x>3 y-7 \Rightarrow y<x+7$ without any explanation given (or if explanation is incorrect) can score M1A0

b1B1: CAO - must see at least 4 x+1<2 y+1 before the given answer of y>2 x and not just arc $\mathrm{AB}<\operatorname{arc}$ AC or 4 x<2 y

b2B1: CAO (x>1) - but allow equivalents, e.g., x-1>0,1<x, 4 x>4, etc. but must be two terms only b3B1: CAO (3 y>4 x+8) - but allow exact equivalents e.g. $y>\frac{4}{3} x+\frac{8}{3}, \quad 4 x-3 y<-8, \quad 4 x+8-3 y<0$, or equivalent but must be three terms only

In (c), the lines can be drawn as either dashed or non-dashed lines (or a combination of the two). The lines must be long enough to define the correct feasible region and pass through one small square of the points stated below:

y=2 x must pass within one small square of (0,0) and (7,14)

y=x+7 must pass within one small square of (0,7) and (7,14)

x=1 must pass within one small square of (1,0) and (1,10)

3 y=4 x+8 must pass within one small square of (1,4) and (7,12)

c1B1: Any one line correctly drawn (ignore any shading)

c2B1: Any two lines correctly drawn (ignore any shading)

c3B1: Any three lines correctly drawn (ignore any shading)

c4B1: All four lines correctly drawn and shading which implies the correct region (but region need not be labelled)

d1B1ft: At least 4 pairs of integer coordinates correctly stated for points inside their region. Thesy mark is dependent on scoring at least the first two marks in (c) (so must have drawn at least two lines corregtly) and the candidate must have drawn exactly four lines. The region must not be infinite but need not ncessaujly be bounded by all four lines. If the candidate's region does not contain 4 integer coordinates then B0. Notechat integer points on the lines that define the boundary of the region are not counted as being inside the regiorisss (regardless of if the candidate has strict inequalities or not)
d2B1: All 9 coordinates correct (and no others) - dependent on all four lines correctly drawn in (c)