(Answered) : (Using excel) A quarry uses five types of rocks to fulfill four orders. The gypsum content, availability of each type of rock, a

(Using excel) A quarry uses five types of rocks to fulfill four orders. The gypsum content, availability of each type of rock, and the production cost per pound for each rock, as well as the size of each order and the minimum and maximum gypsum percentage in each order, are given below.

Rock type——-Cost——-% gypsum——-Amount
1——————-$1.00———–2.0%———–500
2——————-$5.00———–5.0%———–600
3——————-$5.50———–4.5%———–700
4——————-$2.00———–3.0%———–400

5——————-$1.20———–6.0%———–450

Order No.——————–1———-2———-3———4
Order Size——————500——600——500——350
Min % gypsum———–3.5%—–3.8%—–4.0%—–3.6%
Max % gypsum———-4.4%—–4.6%—–4.7%—–4.8%

What is the cheapest way to fill the orders?

Expert Answer

The boxes in green, are decision variables
The boxes in blue are constrains
The boxes in orange is the objective function

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THe formulae used:

Decision Variable, qty in each order
Rock type Cost % Gypsum Order 1 Order

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