A chauffer must decide between driving his client in the Rolls Royce or the Mercedes Benz. The Rolls Royce costs $1.75 per mile to operate and the Mercedes Benz costs $2.00 per mile to operate. The chauffer can charge $4.00 permile for the Rolls and $6.00 for the Mercedes Benz. The chauffer wants his expenses to be no more than 200$ for the day and his total charges to be at least 600$ for the day. The Rolls Royce must travel at most 90 miles and the Merecedes Benz must travel at least 30 miles.

Question

Define the variables

Write the constraints(innequalities)

Write the objective function for the profit.

State the verticies of the region

Evaluate the profit for each point

Identify which car will give the chauffer the maximum profit.

Answer 1

Miles on x axis, dollars on y axis
The Rolls is out.
He must drive at least 150 miles to make 600 dollars Revenue so the region is right of 150 miles or miles >/= 150
BUT
He must drive less than 114.3 miles to cost less than 200. That region is left of 114.3 or Miles </= 114.3
So let's look at the Mercedes
I call MM miles in Mercedes
then
MM >/= 30 corner
cost CM = 2 MM
CM</= 200 so MM <= 100 corner

Revenue Mercedes = RM = 6 MM
Revenue >/= 600 so MM >/= 100 corner

This is a trivial linear programming problem or you have massive typo problems. He must use the Mercedes and drive exactly 100 miles so his cost is $200 and his income is $600.
There is no region surrounded by the constraints. They only meet at that one point and only for the Mercedes.
The profit is RM-CM = 6 MM - 2MM = 600-200 = $400