Product A is sold for 150 whereas product B is priced at 200 There is unlimited

Product a is sold for 150 whereas product b is priced

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Product A is sold for \$1.50 whereas product B is priced at \$2.00. There is unlimited demand for product A but demand for B is limited to 13,000 units per annum. The machine hours available in each department are restricted to 2,400 per annum. Other relevant data are as follows. Machine hours required Mixing Shaping Hrs Hrs Product A 0.06 0.04 Product B 0.08 0.12 Variable cost per unit \$ Product A 1.3 Product B 1.7 The constraints are: 0.06x + 0.08y ≤ 2,400 0.04x + 0.12y ≤ 2,400 y ≤ 13,000 x,y ≥ 0 The objective function is: Contribution (C) = 0.2x + 0.3y The optimal solution is where x = 24,000 and y = 12,000, and total contribution = \$(24,000 × 0.2) + \$(12,000 × 0.3) = \$4,800 + \$3,600 = \$8,400. REQUIRED Calculate the shadow price of an hour of machining time in shaping department and mixing department respectively.

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___________________________________________________________________________________________________________________ Page 11 of 13 IPK COLLEGE 1664, JALAN KULIM, 14202 BUKIT MERTAJAM, PENANG TEL : 012-5203212 / 0125113212 / 04-5512588 Subject: Financial Management (DFM1) Prepared by Chester Chen Email : [email protected] CHAPTER ROUNDUP All companies have a maximum capacity for producing goods or providing services, because there is a limit to the amount of resources available. There is always at least one resource that is more restrictive than others: this is known as a limiting factor . In a situation where a company is able to sub-contract work to make up a shortfall in its own in-house production capabilities , its total costs will be minimised if those units bought from the sub-contractor have the lowest extra variable cost per unit of scarce resource saved by buying. Extra variable cost is the difference between the variable cost of in-house production and the cost of buying from the subcontractor. Linear programming is a technique for solving problems of profit maximisation or cost minimization and resource allocation. 'Programming' has nothing to do with computers: the word is simply used to denote a series of events. If a scenario contains two or more limiting factors , linear programming should be used to determine the contribution-maximising or cost-minimising solution. The graphical method of linear programming can be used when there are just two products (or services). The steps involved are as follows. (1) Define the problem: Define variables Establish constraints Construct objective function (2) Draw the constraints on a graph (3) Establish the feasible region for the optimal solution (4) Determine the optimal solution The optimum solution to a linear programming problem can be found by ‘sliding the iso- contribution line out’. The optimal solution to a linear programming problem can also be found using simultaneous equations Slack occurs when maximum availability of a resource is not used. Surplus occurs when more than a minimum requirement is used. The shadow price or dual price of a limiting factor is the increase in value which would be created by having one additional unit of the limiting factor at its original cost.
___________________________________________________________________________________________________________________ Page 12 of 13 IPK COLLEGE 1664, JALAN KULIM, 14202 BUKIT MERTAJAM, PENANG TEL : 012-5203212 / 0125113212 / 04-5512588 Subject: Financial Management (DFM1) Prepared by Chester Chen Email : [email protected]

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• Spring '17
• JANE KDAL

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