Use graphical method to minimise the time added to process the following jobs on the machines shown:

Rewrite the following linear programming problem in Standard form:
Minimise 
Subject to the Constraints:

The following data comprising the number of customers (in hundred) and monthly sales (in thousand Rupees):

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 d_i ≥ 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.

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:

Solve the following LPP using graphical method:
Maximize 
Subject to the Constraints:

Solve the following LPP using Simplex method:
Maximize 
Subject to the Constraints: