Production Costs When Duffin House printed a million copies of Larry Plotter and the Simplex Method (see Exercise 34), it used print runs of 20,000, which cost the company $880,000. For the sequel, Larry Plotter and the Simplex Method, Phase 2 it used print runs of 40,000 which cost the company $550,000. Use this information to construct a linear model giving the production cost c as a function of the run size n.
a. What is the model?
b. Based on the model, what would print runs of 25,000 have cost the company?
c. Marjory Duffin has decided to budget $418,000 for production of the next book in the Simplex Method series. Based on the model, how large should the print runs be to accomplish this?
Reference:
Production Costs Over at Duffin House, Marjory Duffin is trying to decide on the size of the print runs for the bestselling new fantasy novel Larry Plotter and the Simplex Method. The following model shows a calculation of the total cost to produce a million copies of the novel, based on an analysis of setup and storage costs:
where n is the print run size (the number of books printed in each run).
a. What would be the effect on cost if the run size was increased from 20,000 to 30,000?
b. Would increasing the run size in further steps of 10,000 result in the same changes in the total cost? Explain.
c. What approximate run size would you recommend that Marjoy Duffin use for a minimum cost?
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