A firm plans to begin production of a new small appliance. The manager has three

Question

A firm plans to begin production of a new small appliance. The manager has three options: Option 1: purchase the motors for the appliance from a vendor at $4 each: Option 2: produce them in house using technology A with an annual fixed cost of $150000 and a variable cost of $1 per unit, or Option 3: produce them in house using technology B with an annual fixed cost of $75000 and a variable cost of $3 per unit. The range of output for which Option 1 is best is units. The range of output for which Option 2 is best is units. The range of output for which Option 3 is best is units. FORMAT TO ENTER VALUES: Round to the nearest integer, no decimals Enter the range as #### #### for example: 47500-92000 If an option is outperformed by other option(s), enter NEVER (all capital) For an open ended range use INFINITY (all capital), for example: 47500-INFINITY If an option is good only at one point, just enter the value of the output, for example 8750 DO NOT USE parentheses, spaces or commas!

Explanation / Answer

Lets there are X units are required.

Cost in Option 1 : C = 4x ...(1)

Cost in option 2: C = 150000 + x ....(2)

Cost in option 3 : C = 75000 + 3x ....(3)

equation all 3 equations

(1) and (2)

4x = 150000 + x

x = 50000 units

(2) and (3)

150000 + x = 75000 + 3x

x = 37500 units

(1) and (3)

4x = 75000 + 3x

x = 75000 units

so Option (1) is best in the range of 0 to 50000 units production. [0 - 50000]

Option (2) is best in the range of 5000 to infinity production.[50000 - INFINITY]

OPtion (3) is not best anywhere.

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