In how many ways, can three jobs I, II and III be assigned to three persons A, B and C, if one person is assigned only one job and all are capable of doing each job ? Which assignment of jobs will take the least time to complete the jobs, if time taken (in hours) by an individual on each job is as follows :

A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each on the three machines are given in the following table: SHe makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum Profit?

A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?

Two persons could fit new windows in a house in 3 days : One of the persons fell ill before the work started. How long would the job take now?

Two person can finish the work in 7 days. (i) One of the persons fell ill before the work started . How much time will the other person take to finish the same work. (ii) How many persons will be needed to finish the work in one day.

Three beakers labelles as A, B and C each containing 25 mL of water were taken. A small amount of NaOH, anhydrous CuSO_4 and NaCl were added to the breakers A, B and C respectively. It was observed that there was an increase in the temperature of the solutions containers in beaker A, and B, where in case of beaker C, the temperature of the solution falls. Which one of the following statements(s) is(are) correct? (i) In beaker A and B, exothermic process has occured. (ii)In beaker A and B, endothermic process has occured. (iii) In beaker C exothermic process as occured. (iv) In beaker C endothermic process has occured.

A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling on chair is ₹ 30 while by selling one table the profit is ₹ 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximize profit ? Formulate the problem as L.P.P. and sovle it graphically.

Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1 : 2 : 4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.