Flashcards · 7 cards

Linear programming & operations research

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Rule
Where is the maximum or minimum of $ax + by$ over a region?
Answer
At a corner of the region. Work out $ax + by$ at each corner, or slide the line $ax + by = k$ until it leaves the region.
The best point is a cornerSlide the line ax + by = k out: it leaves the region at a corner
From the lesson: Linear programming
Know it
The steps of a linear programming problem?
Answer
Choose letters for the unknowns. Write each limit as an inequality (with $x, y \ge 0$ ). Draw and shade the region, then test the objective at each corner.
From the lesson: Linear programming
Rule
Maximin and minimax in a payoff matrix?
Answer
Maximin: the largest of the row minima. Minimax: the smallest of the column maxima.
Maximin and minimaxmaximin = largest row minimum; minimax = smallest column maximum
From the lesson: Games, inventory and transport
Know it
When does a game have a saddle point?
Answer
When maximin = minimax. Each player keeps to one strategy, and the value of the game is that entry. Otherwise they mix strategies.
From the lesson: Games, inventory and transport
Rule
The economic order quantity?
Answer
$\text{EOQ} = \sqrt{\dfrac{2DC_o}{C_h}}$ : $D$ the demand, $C_o$ the cost of each order, $C_h$ the holding cost per unit.
Balancing the two costsEOQ = √(2 × demand × ordering cost ÷ holding cost per unit)
From the lesson: Games, inventory and transport
Rule
The north-west corner rule for a transport problem?
Answer
Start at the top-left cell and allocate as much as you can. Move right or down as each supply or demand is used up.
Filling the tableStart top-left; move right or down as each total is used up
From the lesson: Games, inventory and transport
Which method?
WAEC 2020 · Paper 2 · Q4
Shade the region, $P$ , in the $x$ – $y$ plane which satisfies simultaneously the inequalities:

$x + y \ge 5, \qquad 2y - x \ge 0, \qquad x + 5y \le 21$
Use the diagram in 4(a) to find, on the region $P$ , the minimum value of $x$ ;
the maximum value of $(3x + 2y)$ .
How do you find the maximum of $3x + 2y$ on the region?
Answer
Find the corners of the region, where the boundary lines meet, and work out $3x + 2y$ at each. The largest is the maximum.
From the lesson: Linear programming Try the question