Sum

The supply S for a commodity at price P is given by S = P^{2} + 9P − 2. Find the marginal supply when price is 7/-.

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#### Solution

Given, S = P^{2} + 9P – 2

Marginal supply = `("dS")/("dP")`

= `"d"/("dP")("P"^2 + 9"P" -2)`

= `"d"/("dP")("P"^2) + 9"d"/("dP")("P") - "d"/("dP")(2)`

= 2P + 9(1) – 0

= 2P + 9

When P = 7,

Marginal supply =`(("dS")/("dP"))_("P" = 7)`

= 2(7) + 9

= 14 + 9

= 23

∴ Marginal supply is 23, at P = 7.

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