A furniture manaufacturer makes two types of products chairs and tables form his available resorrces processing fo these products is done on two machines `M<_(1)` and `M_(2)` A chair requires 4 hours o machine `M_(1)` and 2 hours on machine `M_(1)` and 2 hour on machine `M_(2)` there are 16 hoiurs of time per day on mcachine `M_(1)` and 10 hours per day on machine `M_(2)` available respectively profits gained by the manufactyurer from a chari and a table are Rs 12 and Rs 9 respectively formulate the problem as a LPP in order to have the maximum profit

A toy company manufacturers two types of dolls, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company make profit of Rs. 12 ad Rs. 16 doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated.It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screw A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit ofRs. 7 and screws B at a profit of Rs. 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

A manufacturer produces two types of articles A and B. The production cost of an article A is Rs.250 and that of B is Rs.300. His total investment does not exceed Rs.20000 and he can store at most 100 articles. Formulate tha given data in the form of inequations and show graphically the region representing the solution of these inequations.

(Manufacturing problem): 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 atleast 5 hours a day. She produces only two items M and N each requiring the sue of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machies are given in the follownig table: She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each item should be 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 cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/ cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour onthe grinding /cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding /cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs. 5 and that from a shade is Rs. 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

(Manufacturing problem): A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hors available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model Aand Rs. 12000 on each piece of Model B. How many piecesof Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

Name two type of essential secretory products of protoplasm.