Profit = Sale price - Cost

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Presentation transcript:

Profit = Sale price - Cost Part (a) Profit = Sale price - Cost Profit = 120x – ∫ 6√x 25 Profit = 120(25) – 4[x3/2] 25 Profit = $2500

Part (b) This represents the cost, in dollars, of building the last five meters of a 30 meter cable.

Profit = Sale price - Cost Part (c) Profit = Sale price - Cost Profit = 120k – ∫6√x k OR Profit = 120k – 4k3/2 P(k) = 4k(30 – √k)

Part (d) Profit is positive on the interval 0 < k < 900, meaning a maximum occurs on this interval when the derivative is zero. From (c)… P(k) = 120k – 4k3/2 P’(k) = 120 – 6√k 0 = 120 – 6√k

Part (d) 0 = 120 – 6√k 6√k = 120 √k = 20 k = 400 Mighty earns maximum profit when they sell a 400 meter cable. Now we have to calculate the profit of the cable.

Part (d) P(400) = 120(400) – 4(400)3/2 P(400) = $16,000