Answer:
To break even it must be molded 1280 handles weekly.
The profit if 1500 handles are produced and sold is $440
Step-by-step explanation:
To break even, the amount of total cost must be the same as the amount of revenues.
Total Cost is Fixed cost plus unitary variable cost multiplied by the produce quantity.
Total cost= FC + vc*Q
Where
FC=Fixed cost
vc=unitary variable cos
Q=produce quantity
Revenue= Price * Q
Break even FC + vc*Q=Price * Q
Isolating Q
FC=(Price * Q)-(vc*Q)
FC=(Price-vc) * Q
Q= FC/(Price-vc)
Q= $2560/($3.00-$1.00)=1280
If we sold 1500 handles
Profit = Revenue- Total cost =(Price * Q)-(FC + vc*Q)
P=$3.00 *1500-$2560 - $1.00*1500=
P=$4500-$2560-$1500=440
Let
x-------> total peanuts originally from the bag
we know that
1) Phillip took 1/3 of the peanuts from the bag--------> (1/3)*x
remaining=x-(1/3)*x-------> (2/3)*x
2) Joy took 1/4 of the remaining peanuts-------> (1/4)*[(2/3)*x]----> (1/6)*x
remaining= (2/3)*x-(1/6)*x------> (1/2)*x
3) Brett took 1/2 of the remaining peanuts------> (1/2)*(1/2)*x-----> (1/4)*x
remaining= (1/2)*x-(1/4)*x-------> (1/4)*x
4) Preston took 10 peanuts------> 10
(1/4)*x-10=71----> multiply by 4 both sides----> x-40=284----> x=324 peanuts
5) Total originally peanuts from the bag is equal to 324 peanuts
6) Phillip took (1/3)*x-----> (1/3)*324=108 peanuts
7) Joy took (1/6)*x------> (1/6)*324=54 peanuts
8) Brett took (1/4)*x------> (1/4)*324=81 peanuts
9) Preston took 10
so
check
108+54+81+10=253
remaining=324-253------> remaining=71-------> is correct
If unrounded the answer would be 607.5 men but if rounded it would be 608 men
