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Q4. Convert the following linear programming problem into dual problem. Maximise Z = 22x1 + 25x2 +19x3 Subject to: 18x1 + 26x2 + 22x3 ≤ 350 14x1 + 18x2 + 20x3 ≥180 17x1 + 19x2 + 18x3 = 205 x1, x2, x3 ≥ 0 Q5. A work shop contains four persons available for work on the four jobs. Only one person can work on any one job. The following table shows the cost of assigning each person to each job. The objective is to assign person to jobs such that the total assignment cost is a minimum. Jobs 1 2 3 4 A 20 25 22 28 Persons B 15 18 23 17 C 19 17 21 24 D 25 23 24 24
Let P (x) be the statement "x can speak Russian" and let
Q(x) be the statement "x knows the computer language
C++." Express each of these sentences in terms of P (x),
Q (x), quantifiers, and logical connectives. The domain
for quantifiers consists of all students at your school.
{x/x is an integer such as x2 =2}
A random variable x has a mean 4 and a standard deviation of 2.what is the corresponding z-score for x=7
A Region of land 50meters by 40meters is to cross diagonally by a road 15meters wide. What is the roads area?
Four coins are tossed. Let A be the random variables representing the numbers of heads that occur. Find the values of the random variables A.
How many rows appear in a truth table for each of these
compound propositions?
a) (q -+ -'p) v (-'P -+ -.q)
b) (p v -.t) /\ (p v -'s)
c) (p -+ r) V (-,s -+ -.t) v (-,u -+ v)
d) (p /\ r /\ s) V (q /\ t) V (r /\ -.t)
At the beginning of the road, a tank truck was traveling full of water in the water tank, but it began to leak. You can assume that the fuel consumption of the truck is directly proportional to the weight it carries, and that the water flow (in the
leakage) and the speed of the truck are constant for the whole journey. After traveling for miles, the truck leaked half of the water from the water tank and consumed half of the fuel tank. If the water tank was empty, the truck would have spent a sixth of the fuel tank, if it travelled the same distance and
under the same conditions as above. Disregarding the fuel tank weight, what fraction of the fuel tank would be spent by the truck if there was no leak?
Answer the question by breaking the problem down into:
assumptions, model and solution/discussion.
The BRIT Sports Bar sells a large quantity of Guinness every Saturday. From past records, the pub has determined the following probabilities for sales:
Number of Crates (X) P(x)
18 0.15
19 0.10
20 0.32
21 0.05
22 0.13
23 0.25
a. Verify that this [P(x)] is a probability distribution.
e. Calculate the variance of the distribution?
f. Determine the standard deviation of the distribution?
Write the probability distribution of the random variable Q defined by the outcomes of rolling a fair die.
