Question

Native Customs sells a popular style of hand-sewn sandal footwear. The cost of making a pair of sandals is $18. The demand for an item is sensitive to the price, and historical data indicate that the monthly demands are given by D(P)= 400 − 10P where D(P) = demand for sandals (in pairs) and P = price for a pair of sandal. To remain competitive, Native Customs must limit the price (per pair) to no more than $35. Formulate this nonlinear programming problem to find the optimal price for sandals that maximize total monthly profit and monthly profit.

1. Define the decision variables

2. Define the objective function

3. Define the constraints

4. Determine an optimal solution.

Answer 1

ANSWER::

a).

Decision Variable: Let P be the price at which the pairs are sold.

if P is the sale price, then profit per pair = P-18

b).

Objective Function: Objective is to maximize the total profit

Zmax = (400-10P)*(P-18)

c).

Constraints:

P <= 35

Solving the LP in solver:

The solver is an excel plug in which can be installed form excel options. After installation, it is available in the data segment of the excel sheet. Once installed and launched, the parameters can be added

Spreadsheet Model along with formula:

Adding Parameters to Solver:

1st: Enter Green highlighted cell (objective function) in the set objective field

2nd: Select Max

3rd: Enter the yellow cells (decision variables) in the by changing variable cells field

4th: In constraints, click on add, enter the blue cells in the dialogue box which appears.

On the left area (cell reference), enter the left side values, select relationships in the middle, and in the right enter the right side values of the inequality signs. Similarly, repeat for the next constraints by clicking on add button. Then click ok to go back to the parameters part.

5th; Select GRG Non linear (selected by default)

6th: Click solve

Solution:

d).

The optimal price is 28.999992 or rounded to 29

Maximum monthly profit = 1210

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