EXPLANATION
Let's see the facts:
Number of weeks = 4
Total cost = rent + utilities + bowls + cones + spoons + employees
Pack cost = $5
Number of spoons by pack = 100
Number of cones by pack = 60
Number of cups by pack = 80
We need to write an equation for the total cost.
Equation for the Total Cost:
Total Cost = rent + utilities + bowls + cones + spoons + employees
We should assign some letters to the variables.
Let's call r to the rent, u to the utilities, b to the bowls, c to the cones, s to the spoons and e to the employees
The equation is as follows:
Total Cost = r + u + b*packs of b + c*packs of c + s*packs of s + employees
As each pack cost 5 usd, we need to add a coefficient:
Total Cost = r + u + 5*packs of b + 5*packs of c + 5*packs of s + employees
To make more simple, let's assign the variables to the packs:
Total Cost = r + u + 5*b + 5*c + 5*s + employees
The given table has the absolute number of cones and bowls, not the packages, so we should consider it on the equation. Representing the equation in function of the absolute number of cones, bowls and spoons:
Total Cost = r + u + 5*b/80 + 5*c/60 + 5*s/100 + employees
We can use the table with the numbers of orders and substitute it on the equation, and with that data, we could assume the total cost.
But first we should depreciate the rent+utilities+employees cost as it's a constant.
We can assume that we need 1 spoon for the cone and 1 spoon for the bowl.
We can build three equations:
(1) small = 5*b/80 + 5*c/60+ 5*(b+c)/100 where b=700 and c=300
(2) medium = 5*b/80 + 5*c/60+ 5*(b+c)/100 where b=1100 and c=800
(3) large = 5*b/80 + 5*c/60 + 5*(b+c)/100 where b=600 and c=200
Replacing terms:
(1) small = 5*700/80 + 5*300/60 + 5*(700+300)/100 where b=700 and c=300
(2) medium = 5*1100/80 + 5*800/60 + 5*(1100+800)/100 where b=1100 and c=800
(3) large = 5*600/80 + 5*200/60 + 5*(600+200)/100 where b=600 and c=200
Multiplying and adding terms:
(1) small = 118.75
(2)medium = 230.41
(3) large = 94.16
Now, we need to divide by the cones+bowls for each size as follows:
(1) small cost/piece = 118.75/(b+c) = 118.75/(300+700) = $0.11875/piece
(2)medium cost/piece = 230.41/(b+c) = 230.41/(800+1100) = $0.1212/piece
(3) large cost/piece = 94.16/(b+c) = 94.16/(200+600) = $0.1177/piece
Hence, we should charge at least:
>$0.11875 for the small size
>$0.1212 for the medium size
>$0.1177 for the larger size (let's suppose $0.13)
Supposing that the utilities+rent+employees cost by each product was of $0.10 by product ,we could charge:
$0.11875+$0.10= 0.21875 for the small size
$0.1212+0.10= 0.2212for the medium size
$0.13+0.10= 0.23 for the larger size
In conclusion, we made in the first month:
1000*0.21875 + 1900*0.2212 + 800*0.23 = $823.03