$16\mathrm{.}01\mathrm{.}2025$

EM$/$IE $301$ Answer Key

$(25$ Points$)$ Use the graphical approach to sensitivity analysis to answer the questions.

Juiceco produces $2$ types of mixed juice from orange, lemon and grape. $40$ kg of orange, $30$ kg of lemon and $40$ kg of grape juice are available. A bottle of the first mix $($Mixture$)$ is sold for $40t$ and requires $100$ g of orange juice, $100$ g of lemon juice and $200$ g of grape juice. A bottle of the second mix $($Mixture$2)$ is sold for $50$ t and requires $200$ g of orange juice, $100$ g of lemon juice and $100$ g of grape juice. Juiceco can sell all the mixed juices produced.

$x1=$ number of bottles of Mixture produced $2=$ number of botlles of Mixture$2$ produced Mathematical

model: maximize $Z=401+502$ such that

$x1+22400($orange juice constraint$)$

$1+2300($lemon juice constraint$)21$

$+x^{2}400($grape juice constraint$)$

$x1,x20$

Let's assume Juiceco's goal is to maximize total sales revenue and solve for the given DP:

a$)$ Find the range of Mix price for which the optimal solution remains the same for the current baseline.

b$)$ Find the range of Mix$2$ prices for which the optimal solution remains the same for the current baseline.

c$.$ Find the range of available orange juice quantities for which the optimal solution for the current baseline remains the same. What is the shadow price of the orange juice constraint?

d$.$ Find the range of available quantities of lemon juice for which the optimal solution for the current baseline remains the same. What is the shadow price of the lemon juice constraint?