A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
Set up the cost function C(t) where t is the number of tons of cattle feed:
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
Set up the revenue function R(t) where t is the number of tons of cattle feed:
R(t) = Sale Price * t
R(t) = 132t
Set up the profit function P(t) where t is the number of tons of cattle feed:
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:
48t - 110000 = 560000
To solve for t, we type this equation into our search engine and we get:
t = 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959
Set up the cost function C(t) where t is the number of tons of cattle feed:
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
Set up the revenue function R(t) where t is the number of tons of cattle feed:
R(t) = Sale Price * t
R(t) = 132t
Set up the profit function P(t) where t is the number of tons of cattle feed:
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:
48t - 110000 = 560000
To solve for t, we type this equation into our search engine and we get:
t = 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959