Question

2. Nordstrom is finalizing its plan for purchasing items for their Super Sale. Their budget is $150,000 and they must decide how many dolars to spend on jewelry, women's clathing, and men's clothing for this sale. Here is how each department sets its selling price: · Jewelry department: selling price = 2 x purchase price Women's clothing department: selling price- 1.5 x purchase price Men's clothing department: selling price = 1.7x purchase price Furthermore, the management requires the following . No more than 30% of the total spending can be spent on jewelry. . No more than 40% of the total spending on clothing can be spent on men's clothing. * The ratio of the total spending on jewery to the total spending an women's clothing should not exceed 50%. Nordstrom expects that everything they purchase for the Super Sale will be sold. Formulate a linear optimization problem to find the optimal total spending (in dolars) for each department a) What are your decision variables? b) Formulate an objective function that will maximize the total profit c What are the constraints? (Write the constraints in the standard form so that all the right hand sides are constants and all the left hand sides are linear functions of the decision variables) The answer report from solving this problem in Excel is shown below. Answer the following questions accordingly. Cel Bss Prof 0 101538.4615 Varable Cells 30615 38462 Contin Women'sc 9230 76923 Contin Cel Value Formula 10 Ratio of men's cl 8s9 Ratio of 10384.61538 90S9 Not 0384.615 d) e) What is the total revenue Nordstrom is expecting from this sale (rounded to the nearest dollar)? How much money will they allocate for clothing purchases (both men's and women's) (rounded to the nearest dollar)?

Answer 1

There are 3 decision variables one for each item. The decision variables reflect the purchase price of each item. Purchase price of jewelry Purchase price of women's clothing x = Purchase price ofmen's clothing b) The objective is to maximize the profit. Profit is equal to the difference of total purchase price and selling price. Thus, the objective function becomes: MaximizeZ = (2x, + 1.55 +17%)-(x, +x2+ c) There are 5 constraints The first constraint is the budget constraint. The total budget is $150,000. Thus: |X, + X2 + X3 $150,000 The second constraint is the jewelry spending constraint.

-0.7% +0.3s +0.3s 20 The third constraint is the men's clothing spending constraint. | 0.3x +0.3x,-0.7% 20 The fourth constraint is the ratio of spending on jewelry and women's clothing.

1, The fifth constraint is the non-negativity constraint. d. The revenue is computed by adding the total purchases to the profit. The total profit = $101,538.4615 Total purchases S34,615.38462+ S69,230.76923+S46,153.84615 $150,000 Thus, the total revenue comes: Total Revenue Total Profit + Total Purchases - $101,538.46150+$150,000 -251 538.46150 $251,539 Thus, the total revenue is S251539

e. The money allocated to clothing is calculated by adding the purchases on women's and men's clothing Money allocated to clothing - $69, 230.76923 S46,153.84615 - $115,385 Thus, the money allocated to clothing is S115,385