Toms Sporting Shop sells two kinds of electric bicycles: The first kind of bicycle is called Ace Race with a unit profit of $250. The other kind is called Big Turbo with a unit profit of $400. Each bicycle of these two kinds requires two sporty tires to be mounted. Tom only has 180 sporty tires available for the month of April. These electric bicycles are powered by high-efficiency batteries. Each Ace Race has one battery installed while each Big Turbo has 3 batteries installed. Tom realized that he only has 120 batteries ordered for his April sales. Since Big Turbo is large in size and the shop space is very limited, Tom can only have at most 30 Big Turbo bicycles in his store for each month. Tom would like to know how many of these two kinds of bicycles to sell in order to maximize his shops profit for the month of April.

1) Formulate this problem as a linear program.

2) Solve graphically for the optimal solution. Describe the optimal solution.

3) What is the profit generated by using the above optimal solution? After you work on the above questions, you receive an update from Tom regarding the price war among the smaller electric bicycles in the market. Thus, the unit profit for the Ace Race is now reduced to $100 while the unit profit for Big Turbo remains $400.

4) What will be your modified optimal solution based on Toms updated information?

5) What is the modified profit?

PLEASE ANSWER EACH # IN LISTED FORMAT and be clear. I need to present this in microsoft word format.THANK YOU!