A soda producer makes and sells two products, Classic Cola and Diet Cola. During
ID: 470293 • Letter: A
Question
A soda producer makes and sells two products, Classic Cola and Diet Cola. During the planning period, if the producer spends x1 dollars on promotion of Classic Cola, it can sell 100x10.5 cases of Classic Cola, and if it spends x2 dollars on promotion of Diet Cola, it can sell 10x20.75 cases of Diet Cola. Each case of Classic Cola sells for $12.00 and costs $0.95 to produce and ship to customers, while each case of Diet Cola sells for $12.50 and costs $1.00 to produce and ship to customers. A total of $7,500 is available for promotion during the planning period.
Formulate and solve a nonlinear optimization model to help this soda producer identify the best promotional strategies for its two products.
Suppose the producer can double the promotional budget. Formulate and solve a nonlinear optimization model to help this soda producer identify the best promotional strategies for its two products in that case. Does the change in profit justify the budget increase? Does the proportional amount spent promoting the two products remain the same?
Explanation / Answer
Maximize the profit =10.05x1 + 9.50x2
Subject to the constraint
100*10.5x1 + 10*20.75x2<110*31.25
1x1+2xx<7500
x1,x2>0
profit calculation
Classic Cola = $0.95 cost +$1 dollars for promotion= $1.95
Diet ColaCost =$1 cost + $ 2 dollars for promotion= $3
Profit = Selling price - cost price
Classic Cola =$12.00 -$1.95=$10.05
Diet ColaCost = $12.50 - $3=$9.50
Optimization strategy
Classic Cola = 1050 units (100* 10.5 cases=1050) * $10.05=$10,552.50 profit
Diet Cola= 207.50 units (10*20.75=207.50)*$9.50=$1,971.25 profit
COST CALCULAITONS
Classic Cola =$1.95* 1050 units =$2047.50
Diet ColaCost = $3* 207.50=$622.75
soda producer best promotional strategies is Classic Cola brings high profit with increase $1 promotional cost but
Diet Cola brings low profit but increase the $2 cost promotional cost.
Classic Cola promotional strategies considered to be good.
_________________________________________________________________________________________
double
Maximize the profit =$9.05x1 + $7.50x2
Subject to the constraint
100*10.5x1 + 10*20.75x2<110*31.25
1x1+2xx<7500
x1,x2>0
profit calculation
Classic Cola = $0.95 cost +$2 dollars for promotion= $2.95($1*2=2double promotion cost)
Diet ColaCost =$1 cost + $ 4 dollars for promotion= $5($2*$2=4double promotion cost)
Profit = Selling price - cost price
Classic Cola =$12.00 -$2.95=$9.05
Diet ColaCost = $12.50 - $5=$7.50
Optimization strategy
Classic Cola = 1050 units (100* 10.5 cases=1050) * $9.05=$9502.50 profit
Diet Cola= 207.50 units (10*20.75=207.50)*$7.50=$1,556.25 profit
Again Classic Cola promotional strategies considered to be good.
No, the profit has decreased when budget amount increased(doubled)
No, the proportional amount spent promoting the two products not same because
$1 is used for Classic Cola and $2 for Diet Cola
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