Question
Asked Dec 11, 2019
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35. Superb Bike Company makes two models of bikes: the Tourismo and the
Racer. Their profit is $10 on a Tourismo and $30 on a Racer. The assembly
department uses 2 hours on each Tourismo and 10 hours on each Racer. At
most 520 assembly hours are available each day. The painting department
can handle at most 100 bicycles per day. The sales department says that
they can sell at most 80 Tourismos and 50 Racers per day. What should
Superb's production be set at?
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35. Superb Bike Company makes two models of bikes: the Tourismo and the Racer. Their profit is $10 on a Tourismo and $30 on a Racer. The assembly department uses 2 hours on each Tourismo and 10 hours on each Racer. At most 520 assembly hours are available each day. The painting department can handle at most 100 bicycles per day. The sales department says that they can sell at most 80 Tourismos and 50 Racers per day. What should Superb's production be set at?

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Expert Answer

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.

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(Objective function) Z=10x +30y .(1) 2.x +10y < 520

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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.

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x<100 and y <100 ..(2) x< 80 and y < 20 .(3)

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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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150 y= 100 100 (10, 50) (80, 36) y = 50 в A (0, 50) 50 (80, 0) 200 250 D O(0,0) 2x+10y=520 50 x= 80 100 x = 100

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