Question

Two automatic systems for dispensing digital topography maps are compared by a geoseismic consulting company.

The accompanying breakeven chart of the comparison of these systems ((System I vs. System II) shows total yearly costs for the number of maps dispensed per year for both alternatives.

$10 - Total cost, System I: y = 0.90x + 1.0 $8 $6 Cost (thousands) Total cost, System II: y = 0.10x + 5.0 $4 $2 $0 0 10 5 Map   

                                                                                                                                                                                           

a) What is the fixed cost for System I?                                                                                                                       

b) What is the fixed cost for System II?                

c) What is the variable cost per map dispensed for System I?

d) What is the variable cost per map dispensed for System II?                                                                             

e) What is the breakeven point in terms of maps dispensed at which the two systems have equal annual costs?

f) For what range of annual number of maps dispensed is System I recommended?

g) For what range of annual number of maps dispensed is System II recommended?

h) At 3,000 maps per year, what are the marginal and average map costs for each system?

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Solution:

Given data:

Two automatic systems for dispensing maps are being compared by the state highway department.

The total cost for system 1 is y1 = 0.9 x + 1.0, and

Total cost for system 2 is y2 = 0.1 x + 5.

a) What are the fixed and variable costs for system 1?

Variable cost = 0.9 Fixed cost = 1

(b) What are the fixed and variable costs for system 2?

Variable cost = 0.1 Fixed cost = 5

(c) What is the number of maps dispensed at which the two systems have equal annual costs?

0.9 x + 1.0 = 0.1 x + 5 0.8x = 4 x=5

(d) For what range of annual number of maps dispensed is system 1 recommended?

0,5

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