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Mathematics Grade 12 Unit 4: INTRODUCTION TO LINEAR PROGRAMMING

national exam questions have come from this unit. It runs 67 pages; one careful study pass takes about 7.2 hours, and its difficulty is harder among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

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4.1 Graphical Solutions of System of Linear Inequalities · read p. 239
  • 2016 E.C., Q13 – Given that a graph of a system of linear inequalities is shown below, which one of the following system of linear inequalities is represented by the shaded region in the graph?
4.2 Maximum and Minimum Values · read p. 260
  • 2018 E.C., Q33 – Which one of the following represents the linear objective function and constraints of the profit? (let S and M be the numbers of Samsung and Motorola mobile respectively)
  • 2018 E.C., Q14 – Given the problem: Maximize $Z=3x+y$ subject to: \[\begin{cases}x+y\ge 2\y+2x\le 4\y\ge 1,\ x\ge 0\end{cases}\] Which one of the following is the maximum value of $Z$?
  • 2018 E.C., Q56 – A farmer having a total capital of Birr 400,000 bought oxen and sheep. An ox costs Birr 60,000 and a sheep Birr 5,000. He sold each ox at Birr 65,000 and each sheep at Birr 6,000. Which one of the following is a represen
  • 2017 E.C., Q37 – Given the objective function $Z=-x+2y$ that is subjected to the constraints $\begin{cases}x\geq 3\x+y\geq 5\x+2y\leq 6\y\geq 0\end{cases}$, what are the maximum and minimum values of $Z$ respectively?
  • 2017 E.C., Q12 – Mr. Bekele finances two investments, $I_1$ and $I_2$. The profits of $I_1$ and $I_2$ are 8% and 10%, respectively. The total investment is Birr one million with at least Birr 50,000 in $I_1$ and at most Birr 300,000 in $
  • 2016 E.C., Q35 – Which one of the following is the minimum value of the following linear programming problem? Minimize: $Z = 3x + y$ Subject to: $y \ge -x + 4, y \ge 5x - 20, x \ge 1, y \le 5$
  • 2015 E.C., Q24 – Which one of the following is the minimum value of the objective function $Z=2x-5y$ subject to the constraints: $3x+2y\leq 6$ $2x+5y\leq 10$ $x\geq 0$ $y\geq 0$
  • 2013 E.C., Q2 – Store-I sells a dozen of pens for 54 Birr and Store-II sells 5 pens of the same brand for 23 Birr. If a clerk wants to buy 100 pens from economical sales, then how much can he save in Birr?
4.3 Applications · read p. 274
  • 2017 E.C., Q24 – Then which one of the following inequalities should model the profit for the objective function Z=1800x+2000y? ⎩ ⎨ ⎧20, 000x + 15, 000y ≤360, 000 ⎩ ⎨ ⎧15, 000x + 20, 000y ≤900, 000
  • 2017 E.C., Q6 – What are the maximum and minimum values respectively of $z = 3x + y$ subject to constraints $\begin{cases} 3x + 2y \leq 20 \\ 2x - y \geq 4 \\ x \geq 0, y \geq 0 \end{cases}$?
  • 2016 E.C., Q36 – If there are at least 400 barrels and at most 1,500 sacks to be transported from the port, which of the z = 8, 000x + 12, 000y following is a constraint of the linear programming problem to minimize the cost of transport