Question

High-tech clothing has become high fashion: Coats with heating technology, solar-powered jackets that charge your phone, dresses that can make payments, health-tracking shirts, LED lighted dresses, inflatable travel wear. You name it, it's out there.... at a hefty price.

You're an entrepreneur and you plan to open a high tech clothing boutique on the Main Line in Philadelphia. You've leased a 2000 sq foot building for your store. You plan to carry 5 product lines; coats, dresses, footwear, shirts, and travel apparel.

About 30% of your floor space will be for aisles, checkouts, dressing rooms and warehousing of inventory. Profitability of the product lines depends on the profit per unit and the inventory turnover rate. (You may be making loads of money on each solar-powered jacket you sell but if you only sell 2 a year, you're not exactly raking in the money.) The products, their annual profit per square foot and annual turnover rate per square foot are given in the table below.

The average annual turnover per square foot-across all product lines-must be at least 45 AND that is based on 2000 square feet. (An average turnover of 45 allows you to at least cover your annual fixed costs.) Coats, dresses and shirts must take up at least 75% of the total square feet used to display your goods.

You must decide how much floor space to allocate to each product line.

Product Type Variable Annual Profit per Square Foot Annual Turnover per Sq Foot
Coats C 110 30
Dresses D 120 60
Footwear F 150 40
Shirts S 125 20
Travel Apparel T 180 10
Formulate the problem. Use the variable definitions in the table. DO NOT SOLVE.
You need not algebraically simply your constraints.

Write your objective function here:

Write your constraints here:

ANS -

So in the question we have the total area of 2000 Square Feet

And Average turnover must be = 45 , So 45 * 2000 = 90000/- for each product

And for 5 Product it will be - 90000 * 5 = 450000/- (Total)

So if we sale for 450000/- rs. we will recovered Annual Fixed Cost

Whereas 75% is for = Coats, dresses and shirts , 25% is for = footwear, and travel apparel And 30% is for = aisles, checkouts, dressing rooms and warehousing of inventory.

So in the terms of Square Feet we can say 600 sqfeet (30%) for Showrooms Display and Warehousing , 1050 sqfeet (75%) for Coats, dresses and shirts And 350 sqfeet (25%) if for Travel apparel & footwear.



So in Resultant/ Conclusion we find out tha If we will sale above the 450000/- then only we can manage the profit else we have to suffer the losses.

Answer 1

Answer:

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