#### Question Details

(solution) You have an idea of selling a new slipper. you need to research

You have an idea of selling a new slipper.

you need to research how much your idea will cost per month and create a function in the form of *C*(*x*)=*mx*+*b* to represent it. where m is the cost of your material and *x* is the number of items produced and *b* is your overhead costs such as rent

Q1. Choose a selling price between $5-$10. Suppose on an average month you sell 500 items.

For every $0.15 increase in your price you sell 10 less items.

Find a function for Revenue, with respect to the number of price increases. Your function will be *R*(*x*) = (number of products sold) x (price).

It is important to incorporate that for every $0.15 in your price you sell 10 less items.

* [Hint: First find a function for the number products sold, and a function for the price of the item.]*

2. Determine the roots of *R*(*x*) and interpret them in the context of the question.

3. Determine the maximum or minimum values of *R*(*x*) and interpret them in the context of the question.

4. Determine the domain and range of and interpret them in the context of the question

5. Create a revenue function with respect to the number of items sold and the new selling price.

6.Using your Cost and Revenue functions, find the profit function, *P*(*x*)=*R*(*x*)?*C*(*x*).Provide all of your calculations and a graph of your profit function.

Q2.

Three planes can intersect in a number of different ways. For the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. (combination)

x ? 3y ? 2z + 3 = 0

-4x + 2y + 3z ? 7 = 0

5x + 4y + z ? 5 = 0

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DATE ANSWEREDSep 13, 2020

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