QUANTITATIVE TECHNIQUES (A1) LINEAR PROGRAMMING PROBLEM (LPP) QUESTION THREE A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item: Item X Y Machine time 13 19 Craftsman time 20 29 The company has 40 hours of machine time available in the next working week but only 35 hours of crafts man time. Machine time is cost at 10 per hour worked and craftsman time is cost at 2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is 20 for X and 30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Required: a) Formulate the problem of deciding how much to produce per week as a linear program. b) Solve this linear- program graphically. COXE C VENANT

A company is involved in the production of two items ( X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item: The company has 40 hours of machine time available in the next working week but only 35 hours of crafts man time. Machine time is cost at 10 per hour worked and craftsman time is cost at 2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is 20 for X and 30 for Y. The company has a specific contract to produce 10items of X per week for a particular customer. Required: a) Formulate the problem of deciding how much to produce per week as a linear program. b) Solve this linear program graphically. A company is involved in the production of two items ( X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item: The company has 40 hours of machine time available in the next working week but only 35 hours of crafts man time. Machine time is cost at 10 per hour worked and craftsman time is cost at 2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is 20 for X and 30 for Y. The company has a specific contract to produce 10items of X per week for a particular customer. Required: a) Formulate the problem of deciding how much to produce per week as a linear program. b) Solve this linear program graphically