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Problem 11

MINING-PRoDucmoN Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs \(\$ 14,000 /\) day to operate, and it yields 50 oz of gold and 3000 oz of silver each day. The Horseshoe Mine costs \(\$ 16,000 /\) day to operate, and it yields 75 oz of gold and 1000 oz of silver each day. Company management has set a target of at least 650 oz of gold and \(18.000\) oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?

Expert verified

To meet the gold and silver extraction targets at a minimum cost, the Saddle Mine should be operated for 4 days and the Horseshoe Mine should be operated for 4 days.

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Chapter 3

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded. $$ \begin{array}{r} x-y \leq 0 \\ 2 x+3 y \geq 10 \end{array} $$

Chapter 3

MANUFACTURING-SHIPPING Costs Acrosonic of Example 4 also manufactures a model G loudspeaker system in plants I and II. The output at plant I is at most 800 systems/month whereas the output at plant II is at most \(600 /\) month. These loudspeaker systems are also shipped to the three warehouses $-\mathrm{A}, \mathrm{B}\(, and \)\mathrm{C}-$ whose minimum monthly requirements are 500,400 , and 400 , respectively. Shipping costs from plant I to warehouse A, warehouse B, and warehouse \(\mathrm{C}\) are \(\$ 16, \$ 20\), and \(\$ 22\) per system, respectively, and shipping costs from plant II to each of these warehouses are \(\$ 18, \$ 16\), and \(\$ 14\) per system, respectively. What shipping schedule will enable Acrosonic to meet the warehouses' requirements and at the same time keep its shipping costs to a minimum?

Chapter 3

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded. $$ \begin{array}{l} 4 x-3 y \leq 12 \\ 5 x+2 y \leq 10 \\ x \geq 0, y \geq 0 \end{array} $$

Chapter 3

Solve each linear programming problem by the method of corners. $$ \begin{array}{ll} \text { Maximize } & P=4 x+2 y \\ \text { subject to } & x+y \leq 8 \\ & 2 x+y \leq 10 \\ & x \geq 0, y \geq 0 \end{array} $$

Chapter 3

MaNUFACTURING-CoLD FoRMULA ProDucmoN Beyer Pharmaceutical produces three kinds of cold formulas: formula I. formula II, and formula III. It takes $2.5 \mathrm{hr}\( to produce 1000 bottles of formula I, \)3 \mathrm{hr}$ to produce 1000 bottles of formula II, and 4 hr to produce 1000 bottles of formula III. The profits for each 1000 bottles of formula I, formula II, and formula III are \(\$ 180, \$ 200\), and \(\$ 300\), respectively. For a certain production run, there are enough ingredients on hand to make at most 9000 bottles of formula I, 12,000 bottles of formula II, and 6000 bottles of formula III. Furthermore, the time for the production run is limited to a maximum of $70 \mathrm{hr}$. How many bottles of each formula should be produced in this production run so that the profit is maximized?

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