Solve the following LPP using graphical method:
Maximize
Subject to the Constraints:
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Rewrite the following linear programming problem in Standard form:
Minimise
Subject to the Constraints:
A department head has four subordinates, and four tasks to be performed. The subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His estimate, of the time each man would take to perform each task, is given in the table below:
| Tasks | Subordinates | ||||||||||||||||||
| E | F | G | H | ||||||||||||||||
| A | 18 | 26 | 17 | 11 | |||||||||||||||
| B | 13 | 28 | 14 | 26 | |||||||||||||||
| C | 38 | 19 | 18 | 15 | |||||||||||||||
| D | 19 | 26 | 24 | 10 | |||||||||||||||
Solve the following LPP using graphical method:
Maximize
Subject to the Constraints:
Use graphical method to minimise the time added to process the following jobs on the machines shown:
| Job 1: | Sequence | A | B | C | D | E | |||||||||||||||||
| Time | 3 | 4 | 2 | 6 | 2 | ||||||||||||||||||
| Job 2: | Sequence | B | C | A | D | E | |||||||||||||||||
| Time | 5 | 4 | 3 | 2 | 6 | ||||||||||||||||||
State whether the following statements are True or False and also give the reason in support of your answer.
a) The Set $ ={(x, y) : 0 ≤ y ≤ 5 when 0 ≤ x≤ 2 and 3≤ y≤ 5 when 2≤ x ≤ 7 } is not a convex set.
b) If 10 is added to each of the entries of the cost matrix of a 3 x 3 assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
c) The solution to a transportation problem with m-rows (supplies) and n-columns
(destinations) is feasible if number of positive allocations is m + n.
d) The Value di ≥ 3 indicates an outlying observation in regression analysis.
e) Variations which occur due to natural forces and operate in a regular and periodic manner over a span of less than or equal to one year are termed as cyclic variations.
Solve the following LPP using Simplex method:
Maximize
Subject to the Constraints:
The following data comprising the number of customers (in hundred) and monthly sales (in thousand Rupees):
| Number of Customers (in hundred) | 4 | 6 | 6 | 8 | 10 | 14 | 18 | 20 | 22 | 26 | 28 | 30 | ||||||||||
| Monthly Sales (in thousand Rs) | 1.8 | 3.5 | 5.8 | 7.8 | 8.7 | 9.8 | 10.7 | 11.5 | 12.9 | 13.6 | 14.2 | 15 | ||||||||||