Question

1. 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: Table 1: Minutes required for each item Item Machine time Crafstman 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 £10 per hour worked and craftsman time is costed 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. • Part (a). Formulate the problem of deciding how much to produce per week as a linear program. • Part (b). Draw the feasible region of your LP formulation. • Part (e). Find the optimal solution of your LP model using graphical solution method. 2. Consider a factory that produces tables. The demand for the tables is known for the coming four months. The manager wants the make a planning of the production quantity in each period. There are two types of costs: cost for each produced table (the production cost) and cost for holding tables in inventory at the at the end of each period (the inventory holding cost). At the start of period 1 there are 5 tables in inventory. The demand and costs per month are given in the following table:

Please show the steps clearly

Answer 1

Solution:

Given

	Machine Time	Craftsman Time
Item X	13	20
Item Y	19	29

Shaded region ABC represents the feasible region

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