# 35. Superb Bike Company makes two models of bikes: the Tourismo and theRacer. Their profit is \$10 on a Tourismo and \$30 on a Racer. The assemblydepartment uses 2 hours on each Tourismo and 10 hours on each Racer. Atmost 520 assembly hours are available each day. The painting departmentcan handle at most 100 bicycles per day. The sales department says thatthey can sell at most 80 Tourismos and 50 Racers per day. What shouldSuperb's production be set at?

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Step 1

As per the question, the profit of Superb is 10 on a Tourismo and 30 on a Racer.

Therefore, let x be the number of units of Tourismo produced in a day and y be the number of units of Racers produced in a day.

The assembly hours required for 1 unit of Tourismo is 2.

The assembly hours required for 1 unit of Racers is 10.

The total number of assembly hours available each day is 520.

First of all, get the objective function as per the condition is given for the profit.

Then, get the first constraint using the given number of hours for assembly.

Step 2

Now, the painting dept can handle at most 100 units per day.

The sales dept. can sale at most 80 units of Tourismo and 50 units of Racers.

By considering the above two conditions get two more constraints.

Step 3

Now plot the graph using constraints 1, 2, and 3 and mark the corner points.

Then feasible region is the region made by the ...

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