Vier-und-Zwanzig GmbH operates a chain of food stores open 24 hours a day. Each store has a standard 4000 square metres of floor space available for merchandise. Merchandise is grouped in two categories: grocery products and dairy products. Vier-und-Zwanzig requires each store to devote a minimum of 1000 square metres to grocery products and a minimum of 800 square metres to dairy products. Within these restrictions, each store manager can choose the mix of products to carry.

The manager of the Salzburg store estimates the following weekly contribution margins per square metre: grocery products, €100; dairy products, €30.

Required

1. Formulate the decision facing the store manager as an LP model. Use G to represent square metres of floor space for grocery products and D to represent square metres of floor space for dairy products.

2. Why might Vier-und-Zwanzig set minimum bounds on the floor space devoted to each line of products?

3. Compute the optimal mix of grocery products and dairy products for the Salzburg store.

4. Will the optimal mix determined in requirement 3 change if the contribution margins per square metre change to grocery products, €80, and dairy products, €50?