SOLUTION: 1 )The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening c

Question 733627: 1 )The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening company will charge $195 set up fee and $3.50 per
T-shirt ordered. The PTA is charging $5 per shirt to students.
a. Write an equation for the total cost, C, of ordering t T-shirts. b. b. Write an equation for the revenue, R, for selling t T-shirts.
c. Write an equation for the profit, P, made by the PTA for selling the shirts.
d. (1 point) How many shirts does the PTA have to sell before they start making money for their fundraiser?
e. (1 point) If the PTA needs to raise $5000 for the new track field, how many T-shirts do they need to sell?

Answer by chana(69) (Show Source): You can put this solution on YOUR website!
1)The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening company will charge $195 set up fee and $3.50 per
T-shirt ordered. The PTA is charging $5 per shirt to students.
a. Write an equation for the total cost, C, of ordering t T-shirts. b. b. Write an equation for the revenue, R, for selling t T-shirts.
c. Write an equation for the profit, P, made by the PTA for selling the shirts.
d. (1 point) How many shirts does the PTA have to sell before they start making money for their fundraiser?
e. (1 point) If the PTA needs to raise $5000 for the new track field, how many T-shirts do they need to sell?
Ans:
Consider fixed cost(FC)= 195$
Cost pice = 3.50$
Selling price = 5$
a.total cost = t*3.50 + 195
Where t= no of shirts ordered .
total cost and fixed cost .The above question is answered on the basis that all the expense includes FC+Variable cost
Where variable cost here is cost of one shirt *total ordered.
b.Revenue= t*5$
where t= toal shirts ordered.
c.P = revenue - Total cost
=(t*5)-(t*3.50 + 195)
d.this is calculated by using break even point, in that point there will be no profit and no loss, after this poin, the company faces profit.
break even quantity = FC/(CP-SP per unit)
=195/(5-3.5)
=130 shirts.
So this company have to sell 130 shirts to make a profit.
e.use this formula P = Total revenue - total cost
5000= (X*5)-(X*3.50 + 195)
Where X is the total number of shirts to be sold to attain a profit of 5000$
Solving for X we get 3203 (rounded for nearest whole number)i.e., number of shirts to be sold.

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