## (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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Sep 13, 2020

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