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Matthew Bailey, as manager of Designs by Bailey, is upgrading his CAD software. The high-performance (HP) software rents for $3,000 per month per workstation. The standard-performance (SP) software rents for $2,000 per month per workstation. The productivity figures that he has available suggest that the HP software is faster for his kind of design. Therefore, with the HP software he will need five engineers and with the SP software he will need six. This translates into a variable cost of $200 per drawing for the HP system and $240 per drawing for the SP system. At his projected volume of 80 drawings per month, which system should he rent?

Respuesta :

Using linear functions, it is found that the high-performance system should be rented.

A linear function has the following format:

[tex]y = ax + b[/tex]

In which:

  • a is the slope, which is the variable cost.
  • b is the y-intercept, which is the fixed cost.

With the high-performance software:

  • Fixed cost of $3,000 per month, hence [tex]b = 3000[/tex].
  • Cost of $200 per drawing, hence [tex]a = 200[/tex]

Then, the model is:

[tex]C_{hp}(d) = 3000 + 200d[/tex]

With the standard-performance software:

  • Fixed cost of $2,000 per month, hence [tex]b = 2000[/tex].
  • Cost of $240 per drawing, hence [tex]a = 240[/tex]

Then, the model is:

[tex]C_{sp}(d) = 2000 + 240d[/tex]

The costs for 80 drawings, that is, [tex]d = 80[/tex] for both cases are given by:

[tex]C_{hp}(80) = 3000 + 200(80) = 19000[/tex]

[tex]C_{sp}(80) = 2000 + 240(80) = 21200[/tex]

Due to the lower cost, the high-performance system should be rented.

A similar problem is given at https://brainly.com/question/20849340

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