$11$:$48$

$24$

The average cost to produce $x$ units of a lacrosse stick is given by $v(x)=250\mathrm{.}25x0\mathrm{.}05x^2,$ where $v(x)$ is in dollars per unit. These are sold in bulk, where the sale price in dollars per stick is $s(x)=199-0\mathrm{.}45x0\mathrm{.}04x^2.$

a$.$ Find the Cost, Revenue, and Profit models when $x$ units are produced and sold.

$C(x)=25x0\mathrm{.}25x^{2}0\mathrm{.}05x^3$

$R(x)=$

$P(x)=$

b$.$ Find the marginal cost, marginal revenue, and marginal profit when $50$ sticks are produced and sold using the formulas $C(x1)-C(x),R(x1)-R(x),$ and $P(x1)-P(x).$

Search

$(1)$

$($

b$.$ Find the marginal cost, marginal revenue, and marginal profit when $50$ sticks are produced and sold using the formulas $C(x1)-C(x),R(x1)-R(x),$ and $P(x1)-P(x).$

Marginal cost: $$

Marginal revenue: $$-157\mathrm{.}49$

Marginal profit: $ $$

c$.$ Use derivatives to estimate the marginal cost, marginal reven$$e$,$ and marginal profit when $50$ sticks are produced and sold.

Marginal Cost: $ $$

Marginal Revenue: $$

Marginal Profit: $ $$

Search