57. A beer company has divided Bloomington intotwo territories. If the company spends x1 dollarson promotion in territory 1, it can sell 60x11y2 casesof beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x21y2 cases of beerthere. 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 andincurs $4 in shipping and production costs. A total of$5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, byapproximately how much would the company’sprofit increase? By how much would its revenueincrease?c. Use SolverTable to see how a change in the priceof beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.
57. A beer company has divided Bloomington into
two territories. If the company spends x1 dollars
on promotion in territory 1, it can sell 60x1
1y2 cases
of beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x2
1y2 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 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.
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