# \$370 a month. Each of Cindy's cupcakes will cost \$3 to produce. She plans to charge \$5 percupcake. Let x represent the number of cupcakes produced and sold.11. Cindy wants to open a cupcake stand. She estimates that the cost of operating the stand will bea. Write down the cost function C (x).b. Write down the revenue function R(x).c. Write down the profit function P(x).d. How many cupcakes does Cindy need to sell to break-even?12. Cindy wants to make more profit on her cupcake stand so she hired a market analyst. The analystdetermined that Cindy had accurately estimated her costs (see problem 11) and that her price-demand function is given by p(x) = 6.8 – 0.001xwhere xis the number of cupcakes produced and sold.0SxS 3000. Find the new revenue function for Cindy's cupcake stand.Find the new profit function for Cindy's cupcake stand and determine its domain.How many cupcakes does Cindy need to sell now in order to break-even?76 ull LTE O10:40Columbia - Harpers ChoiceEditToday 10:39 PMUodgersMethe KokkonattaGrapio1 bed. Determine how many cupcakes Cindy should sell in order to maximize her profits.e. What price should Cindy charge in order to maximize her profit?QUITMODESTA

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Step 1

Cost function is the function which is related to all of the cost that is being spent on the production and maintenance.

Revenue function is the function which is related to all the cost that is being received after selling the product.

Profit function is the difference of the revenue function and cost function.

Step 2

a) Assume number of cupcakes =x

So, if 1 cupcake is made at \$3. So, x cupcakes will be made is \$ 3x.

Also, additional \$370 is added for the rent. Thus, cost function will  be,

C(x)=3x+370

Step 3

b) 1 cupcake is sold for \$5. So, x cupcakes is sold for \$ 5x....

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