A pharmaceutical company requires everyday 10,12,12 units of chemicals `C_1,C_2 and C_3` respectively. A liquid product contains 5,2,and 1 units of chemicals `C_1, C_2 and C_3` respectively per bottle and its cost is Rs.300 per bottle. A dry product contains 1,2 and 4 units of chemicals `C_1, C_2 and C_3` respectively per box and it costs Rs.200 per box. how much quantitiy of either of the two products should be purchased daily in order to minimize the cost.

Food X contains 6 units of vitamin A per g and 7 units of vitamin B per g and costs Rs 2 per g. Food Y contains 8 units of vitamin A per g and food Y contains 8 units of vitamin A per g and 12 units of vitamin B per g and costs Rs 2.50 per g. The daily minimum requirement of vitamin A and vitamin B are 100 units and 120 uniys respectively. Formulate the above as a LPP to minimize the cost.

An oil company requires 13000, 20000 and 15000 barrels of high grade, medium grade and low grade oil respectively, Refinery A produces 100, 300 and 200 barrels per day of high, medium and low grade oil respectively whereas refinery B produces 200, 400 and 100 barrels per day respectively. If A costs Rs 400 per day and B costs Rs 300 per day to operate, how many days should each be run to minimise the cost of requirement?

P= A^3. B^(1/2) . C^1 . If percentage errors in A, B and C are 1, 2 and 4 respectively, then find the percentage error in P.

A soft drinks firm has two bottling plants, one located at P and the other located at Q. each plant produces three different soft drinks A, B and C. The capacities of two plants in number of bottles per day, are as follows: A market survey indicates that during the month of April, there will be a demand of 24000 bottles of A, 16000 bottles of B and 48000 bottles of C. The cost of running the two plants P and Q are respectively Rs.6000 and Rs.4000 per day. find graphically, the number of days for which either of the two plants P and Q should be run in the month of April so as to minimize production cost while still meeting the market demand.

A soft drinks firm has two bottling plants, one located at P and the located at Q. Each plant produces three different soft drinks A, B and C. The capacities of two plants in number of bottles per day, are as follows: A market survey indicates that during the month of April, there will be a demand for 24000 botlles of A, 16000 bottles of B and 48000 bottles of C. The cost of running the two plants P and Q are respectively Rs 6000 and Rs 4000 per day. Find graphically, the number of days for which either of the two plants P and Q should be run in the month of April so as to minimise production cost while still meeting the market demand.

There are two factories located one at place P and the other at place Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A, B and C. The weekly requirements of the depots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is given below : How many units should be transported from each factory to each depot in order that the transportable cost is minimum. When will be the minimum transportation cost?

An oil company requires 12000, 20000 and 15000 barrerls of high grade, medium grade and low grade oil respectively. Refinary A produces 100,300 and 200 barrerls per day of high, medium and low grade oil respectively whereas refinary B produces 200,400,100 barrels per day respectively.If A costs Rs.400 per day and B Rs.300 costs per day to operate, how many days should each refinery be run to minimize the cost of meeting requirements.

Prove that 1 + ^3C_1+ ^4C_2= ^5C_3 .