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In: Math

Jon Hoke owns a bicycle shop. He stocks three types of bicycles: road-racing, cross-country and mountain....

Jon Hoke owns a bicycle shop. He stocks three types of bicycles: road-racing, cross-country

and mountain. A road-racing bike costs $1,200, a cross-country bike costs $1,700 and a

mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100

and mountain bikes for $1,200. He has $12,000 available this month to purchase bikes. Each

bike must be assembled: a road-racing bike requires 8 hours to assemble, a cross-country bike

requires 12 hours and a mountain bike requires 16 hours. He estimates that he and his

employees have 120 hours available to assemble bikes. He has enough space in his store to

order 20 bikes this month. Based on past sales, John wants to stock at least twice as many

mountain bikes as the other two combined because mountain bikes sell better. Formulate

(develop the objective function and constraints) a linear programming model for this problem

where the Jon’s objective is to maximize total profits. Generate the solution using Excel Solver.

Please include Solver explanation. (step by step)

Solutions

Expert Solution

Let X,Y Z be the quantities of road-racing, cross-country and mountain bikes respectively that John stocks.

These are the decision variables.

The total profit of producing/selling X,Y Z be the quantities of road-racing, cross-country and mountain bikes is

Jon’s objective is to maximize total profits and hence the above is the objective function

Now the constraints

He has $12,000 available this month to purchase bikes. The total cost of purchasing X,Y,Z quantities needs to be not more than $12,000

employees have 120 hours available to assemble bikes. The total time needed to assemble X,Y,Z quantities needs to be within this

He has enough space in his store to order 20 bikes this month.

Based on past sales, John wants to stock at least twice as many mountain bikes (Z) as the other two combined (X+Y) because mountain bikes sell better

The LP model is

maximize

s.t.

Prepare the following sheet

get this

setup the solver using data-->solver

get this

John needs to stock 3 quantities of road-racing and 6 quantities of mountain to maximize the profit. The optimum profit at this stocking level is $3,600

milcah answered 1 year ago
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