# A firm plans to begin production of a new small appliance. The manager has three options: Option 1

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 \$5 each: Option 2. produce them in house using technology A with an annual fixed cost of \$95000 and a variable cost of \$3 per unit, or Option 3: produce them in house using technology B with an annual fixed cost of \$35000 and a variable cost of \$4 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 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 commasl

Fixed cost of option 1 is 0 and Variable cost is \$ 5. Next lower variable cost is \$ 4 of option 3. Therefore,

The upper limit of output for which option 1 is best = (Fixed cost of option 3 – Fixed cost of option 1) / (Variable purchase cost of option 1 – Variable cost of option 3)

= (35000 – 0) / (5-4) = 35000 units

The range of output for which option 1 is best = 0 – 35000 units

The lower limit of output for which option 2 is best = (Fixed cost of option 2 – Fixed cost of option 3) / (Variable purchase cost of option 3 – Variable cost of option 2) = (95000 – 35000) / (4 – 3) = 60000 units. Therefore,

The range of output for which option 2 is best = 60000-INFINITY units

The range of output for which option 3 is best = 35000-60000 units   (in between option 1 and 2)

We can also determine these ranges with the help of graph as below

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