A beer company has divided Bloomington into two territories. If the company spends x 1 dollars on promotion in territory 1, it can sell 60x 1 1/2 cases of beer there; and if it spends x 1 dollars on...

A beer company has divided Bloomington into two territories. If the company spends x₁
dollars on promotion in territory 1, it can sell 60x₁
^1/2
cases of beer there; and if it spends x₁
dollars on promotion in territory 2, it can sell 40x₂
^1/2
cases of beer there. Each case of beer sold in territory 1 sells for $10 and incurs $5 in shipping and production costs. Each case of beer sold in territory 2 sells for $9 and incurs $4 in shipping and production costs. A total of $5000 is available for promotion.


a.  How can the beer company maximize its profit?

b.  If an extra dollar could be spent on promotion, by approximately how much would the company’s profit increase? By how much would its revenue increase?


c.  Use SolverTable to see how a change in the price of beer 1 affects the optimal solution. Do the same for a change in the price of beer 2.