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A certain company sells and ships bulk dried foods using the following pricing scheme. They charge $3 per pound for the first 10 pounds, $1.50 for the next 10 pounds and $.50 per pound for any remaining amount, up to 40 pounds. Shipping charges are $7.50 for packages up to 10 pounds and $12 for packages over 10 pounds. Write a piece-wise function showing the cost f(x) to buy and ship x pounds of dried foods from the company described above. Then, graph the function

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f(x) as a piecewise function would be:


f(x) = ($3/lb)x, for 0≤x≤10,
      = ($1.50/lb)x, for (10,20], and
      = ($0.50/lb)x, for (20,40]
       To the above must be added $7.50, [0,10] or $12, (10,40]

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