I answered some of the questions but i need help with number 7, 8, and 10. Here is an example of the assignment.
I am the current secretary of a horse rescue, in charge of fund raising as well as organization and meeting minutes. We have decided to increase the annual membership fee. We have discovered that there is a demand curve for payments. (A demand curve is how much people will pay for an item based on its availability in the open market.) Many times this is found through trial and error.
1. Suppose that we learn that when the membership fees are $20 annually, we have 11 people sign up to be members. But, when we charge $10 per month, we have 7 people sign up. Write a demand equation using the form p=mx+b.
Demand equation is
The revenue is the amount earned from an item before business costs are deducted. To find the revenue of a product, we can multiply the demand equation (p) by the quantity sold (x).
2. Find the demand equation for our revenue from membership by substituting the equation from part A into the equation R=px. Don’t forget to simplify!
The costs of our nonprofit can be found by adding our fixed costs to our variable costs for each horse. Our fixed costs for the rescue is the rental of the property, which is $250 monthly. Our variable costs are for feed and hay, which is $50 per horse per month.
3. If “b” represents the fixed cost, which value would b represent?
4. Write the equation for the cost for each horse per month, using the equation C = mx+b
5. What would our total cost be for 14 horses in a given month?
6. If our total cost is $1300 for a given month, how many horses were housed in the rescue in that month?
The horse rescue’s only means of support is fundraising and donations. In a given month, the rescue will hold several fund raisers at restaurants that will donate 20% of the food sales on a given evening to the rescue.
7. If we have 17 horses in a given month, how much would the restaurants have to make in sales for us to break even?
Restaurant would have to make dollars to break even.
8. We also need to save up during the summer months to purchase extra hay for the winter. If we still have the same 17 horses, how much revenue would the restaurant have to make in order for use to save $200?
9. In a given year, a local feed chain will make a profit of $96,000,000. Write this in scientific notation.
10. We decide to make a triangular pen for a few of the horses out of some spare fencing. The current field is fenced in the shape of a rectangle. We use a corner of the existing fence, so the two existing sides are 18 feet and 22 feet. How much fencing will we need to connect the two sides? (Round to the nearest tenth, if necessary.)
To solve question 7, 8, and 10, we need to follow the given instructions.
Question 7:
To find the sales required for the rescue to break even, we need to set the cost equal to the revenue.
First, we find the total cost for the given month using the equation C = mx + b, where b represents fixed cost.
Next, we substitute the value of cost (C) with $1300 and the value of 17 horses into the equation to find the value of b.
Once we have the value of b, we use the demand equation (from question 1) to calculate the revenue required to break even by setting it equal to the cost equation. We solve for x, which represents the sales the restaurant needs to make.
Question 8:
We need to calculate the revenue required by the restaurant in order for the rescue to save $200.
Using the same demand equation, we substitute the value of the cost ($1300) into the equation to find the corresponding value of x (sales).
Once we have the value of x, we add $200 to the cost to calculate the new total cost.
Next, we substitute the new total cost and the value of 17 horses into the equation to find the value of b.
Finally, we use the demand equation to calculate the revenue required by the restaurant by setting it equal to the new cost equation. We solve for x.
Question 10:
We are given two sides of a rectangle, 18 feet and 22 feet.
To find the length of the additional side needed to connect the two sides, we can use the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the two known sides and c is the length of the unknown side.
Substitute the values into the equation and solve for c, which represents the additional fencing needed to connect the two sides.