The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at $100 per hour worked and craftsman time is costed at $20 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is $200 for X and $300 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer.

$21357

Explanation:

The table below gives the number of minutes required for each item

                             Machine time              Craftsman time

Item X                        13                              20

Item Y                        19                               29

The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at $100 per hour worked and craftsman time is costed at $20 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is $200 for X and $300 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Formulate the problem of deciding how much to produce per week as a linear program hence make the decision.

Let be the number of items of and be the number of items of .

We need to maximize:

200 + 300 − 100(ℎ ) − 20( )

subject to:

13 + 19≤ 40(60) ℎ

20 + 29≤ 35(60)

≥ 10

,≥ 0

The object function is now:

the maximum occurs at the intersection of =10 and  20 + 29≤ 2100.

Solving simultaneously, we have that =10 and =65.52. Substituting in the objective function:

197.1667(10) + 295.8667(65.52)=$21357

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