Question

A) Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $16,000/day to operate, and it yields 60 oz of gold and 3000 oz of silver each day. The Horseshoe Mine costs $18,000/day to operate, and it yields 80 oz of gold and 1250 oz of silver each day. Company management has set a target of at least 700 oz of gold and 17,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost C in dollars? Minimize C = ___ subject to the constraints: gold = _ silver = _ x ≥ 0 y ≥ 0 B) Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast iron and 7 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $1.50, and the profit for each model B grate is $1.00. 1400 lb of cast iron and 1200 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars? Maximize P = _ subject to the constraints: cast iron = _ labor = _ model A = _ y ≥ 0 C) Formulate but do not solve the following exercise as a linear programming problem. Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type A vessel, x, has 60 deluxe cabins and 165 standard cabins, whereas a type B vessel, y, has 80 deluxe cabins and 110 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 350 deluxe and 670 standard cabins for their 15-day cruise in May. It costs $44,000 to operate a type A vessel and $52,000 to operate a type B vessel for that period. How many of each type of vessel should be used in order to keep the operating costs, C (in dollars), to a minimum? Minimize C = _ subject to the constraints: deluxe cabins = _ standard cabins = ___ x ≥ 0 y ≥ 0

A) Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $16,000/day to operate, and it yields 60 oz of gold and 3000 oz of silver each day. The Horseshoe Mine costs $18,000/day to operate, and it yields 80 oz of gold and 1250 oz of silver each day. Company management has set a target of at least 700 oz of gold and 17,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost C in dollars?

Minimize C = _______ subject to the constraints:
gold = _______
silver = _______
x ≥ 0
y ≥ 0

B) Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast iron and 7 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $1.50, and the profit for each model B grate is $1.00. 1400 lb of cast iron and 1200 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars?

Maximize P = _______ subject to the constraints:
cast iron = _______
labor = _______
model A = _______
y ≥ 0

C) Formulate but do not solve the following exercise as a linear programming problem. Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type A vessel, x, has 60 deluxe cabins and 165 standard cabins, whereas a type B vessel, y, has 80 deluxe cabins and 110 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 350 deluxe and 670 standard cabins for their 15-day cruise in May. It costs $44,000 to operate a type A vessel and $52,000 to operate a type B vessel for that period. How many of each type of vessel should be used in order to keep the operating costs, C (in dollars), to a minimum?

Minimize C = _______ subject to the constraints:
deluxe cabins = _______
standard cabins = _______
x ≥ 0
y ≥ 0

Added by Juan Jos- R.

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