Question

In: Operations Management

The fixed and variable costs for three potential manufacturing plant sites for a rattan chair weaver...

The fixed and variable costs for three potential manufacturing plant sites for a rattan chair weaver are shown

PART (A)

A business is trying to decide what facility to use to produce its products. In the following table you have fixed and variable costs listed for each of three facilities.

Site	Fixed Cost per Year	Variable Cost per Unit
1	$500.00	$11.00
2	$1,000.00	$7.00
3	$1,700.00	$4.00

Over what range of production is each location optimal? Clearly show your graph as well as specify range of production for each site. PLEASE USE EXCEL FOR THIS PROBLEM.

PART (B)

If the production is 200 units, which site is the best?

Expert Solution

Part A

Let x be the number of units produced. For each site the total cost can be modelled as per the following equations on the principle that total cost is equal to Fixed Cost plus variable cost

Site 1 : y = 500 + 11*x

Site 2 : y = 1000 + 7 *x

Site 3 : y = 1,700 + 4*x

We can see that these lines have a reducing slope and meet each other at 3 distinct points which can be determined by solving the 3 sets of simultaneous equations.

Solvinf 1 and 2 together we get x = 125, y = 1875. Solving 2 and 3 together we get x = 700/3 = 233.33 , y = 5200/3 = 2633.33 and solving 3 and 1 together we get x = 1200/7 = 171.42 , y = 1885.71.

Hence we see that site 1 is optimal for production less than 125, Site 2 between 125 and 233.33, and Site 3 for x > 233.33.

Part B :

For x = 200. Site 2 is the best at Cost = 1000 + 7*200 = 2400. Site 1 at 200 units will be 500 + 11*200 = 2700 and Dite 3 will be 1700 + 4*200 = 2500.

The graph is illustrated below

keosha answered 4 months ago

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