Exercise $1$: Construct a mathematical model of an integer programming pro$-$

blem and use Solver to nd the optimal solution $($don$\text{'}$t forget to add integer

constraints in the Constraints$)$:

a$)$ Potato Problem

A food company processes potatoes. Its products are potato chips, sold at $120$

CZK$/kg,$ and french fries at $76CZ\frac{K}{k}g.$ To produce $1kg$ of chips, $2kg$ of po$-$

tatoes and $0\mathrm{.}4$ liters of oil are consumed, and to produce $1kg$ of fries, $1\mathrm{.}5kg$ of

potatoes and $0\mathrm{.}2$ liters of oil are consumed. Design a production program to ma$-$

ximize PROFIT $($ignoring labor costs, energy, etc.$)$ with raw material purchase

prices of $12CZ\frac{K}{K}g$ for potatoes and $40CZ\frac{K}{l}$ for oil, while not exceeding the

supplier's capacity $(100kg$ of potatoes and $16$ liters of oil$).$ How will the optimal

solution change if the buyer is willing to purchase goods only in packages

for chips and $15kg$ for fries$)?$