$2\mathrm{.}2$ Solution using solver $(10\%)$

Assume that the manufacturer adds hybrid vehicles to their range, which generate

$2,500$ profit per car. The hybrid cars use about the same number of semiconductors as the EVs, and the plant can assemble them at the same rate as the ICE cars

$($i$.$e$.$ producing maximum $1,200$ hybrids in $3$ days and no other types of cars$).$

Your task is to:

$1.$ Write the updated objective function. $1$ mark

$2.$ Write the updated constraints for supplies and production $($do not forget

about the contract to produce $100$ ICE cars$).2$ marks

$3.$ Find the solution $($an optimal combination of three types of cars$)$ and the

optimal value $($the maximum profit$)$ to this problem. Here, you can use the

lpSolve library in R$.$ Include your code into the report. $5$ marks

$4.$ What happens if the company secures up to $3,000$ boxes of semiconductors

per day? What will be the solution and the maximum profit in this case? $2$ marks