LINEAR PROGRAMMING CSEC QUESTIONS
1. January 2019
Mr. Thomas makes x bottles of juice y cakes daily. To supply his
customers, he makes at least 20 bottles of juice and no more than
15 cakes each day.
(i)
Write TWO inequalities to represent this
information.
(ii) Each day, Mr. Thomas uses $163 to make the bottles of
juice and the cakes. The cost to make a bottle of juice is
$3.50 and the cost to make a cake is $5.25. Write an
inequality to represent this information.
(iii) Show that on an y given day, it is not possible for Mrs.
Thomas to make 50 bottles of juice and 12 cakes.
2. July 2021
Marla buys 2 types of mobile phones., B-Flo and C-Flex, from a
company to retail. One B-Flo mobile phone costs $60 while one
C-Flex costs $80. She buys x number of B-Flo phones and y
number of C-Flex phones.
(i) Marla must NOT spend more than $1,200. Write an
inequality to represent this information.
(ii) The number of B-Flo phones must be greater than or
equal to the number of C-Flex phones. Write an
inequality in and y to represent this information.
(iii) Represent the two inequalities on a graph paper using
the scale 2cm:5units on each axis. Label as R, the region
that satisfies both inequalities.
(iv) The total number of phones is represented by x+y.
According to the graph, what is the largest possible
value of x+y?
3. June 2010
(vii)The cost of an orange is $25 and a mango is $50.
Write an expression to represent the total cost for
buying the fruits.
(viii) Calculate the minimum amount Trish would pay for
fruits.
5. January 2004
(a) Mrs. Singh owns a clothing store. She buys x dresses and y
shirts from a factory at wholesale prices.
(i) For a wholesale purchase, she must buy AT LEAST 15
dresses and AT LEAST 20 shirts. Write TWO inequalities to
represent this information.
(ii) Mrs. Singh has $2 400 to spend on the dresses and shirts.
Each dress costs $40 and each shirt costs $30. Write an inequality
to represent this information.
(b) Using a scale of 1 cm to represent 5 units on each axis, draw a
graph of the THREE inequalities and label the region R, which
satisfies ALL of the inequalities.
(c) Mrs. Singh sells the dresses and shirts in her store. She makes
a profit of $25 on each dress and $6 on each shirt.
(i) Write an expression for the profit, P.
(ii) Determine the number of dresses and shirts that Mrs. Singh
should buy to make the maximum profit.
(iii) Calculate the maximum profit.
A farmer supplies his neighbors with x pumpkins and y melons
6. May 2012
daily, using the following conditions:
A florist makes bouquets of flowers, each consisting of 𝑥 roses
First condition: 𝑦≥3
and 𝑦 orchids. For each bouquet, she applies the following
Second condition: 𝑦≤𝑥
Third condition: the total number of pumpkins and melons must constraints:
1. The number of orchids must be at least half the
not exceed 12
number of roses.
(i)
Write an inequality to represent the THIRD
2. There must be at least 2 roses.
condition.
3. There must be no more than 12 flowers.
(ii)
Using a scale of 1cm to represent one pumpkin on
(i) Write THREE inequalities for the constraints given.
the x-axis and 1 cm to represent 1 melon on the
(ii) Draw the graph of the THREE lines representing the
y-axis, draw the graphs of the THREE lines
THREE inequalities above.
associated with the THREE inequalities.
(iii) Shade the region that represents the solution set for the
(iii)
Identify, by shading, the region which satisfies the
THREE inequalities.
inequalities, label it R.
(iv)
Determine, from your graph, the minimum value of
(iv) State the coordinates of the points which represent the
x + y.
vertices of the region showing the solution set.
(v) The florist sells a bouquet of flowers to make a profit of
4. May 2013
$3 on each rose and $4 on each orchid. Determine the
Trish wishes to buy x oranges and y mangoes which she intends to
MAXIMUM possible profit on the sale of a bouquet.
carry in her bag. The bag has space for only 6 fruits.
(i) Write an inequality to represent this information.
(ii) To get a good bargain, she must buy AT LEAST 2
mangoes. Write an inequality to represent this
information.
(iii) More information about the number of oranges and
mangoes associated with the good bargain is represented
by 𝑦 ≤ 2𝑥. Write the information represented by this
inequality as a sentence in your own words.
(iv) Draw the lines associated with the inequalities above.
(v) Shade on your graph the region which represents the
solution set for the three Inequalities.
(vi) List the set of coordinates of the vertices that bound
the feasible region.
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