# Chapter 2 Assignment questions and answers

**Topics:**Optimization, Linear programming, Maxima and minima

**Pages:**4 (623 words)

**Published:**February 23, 2015

1. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 20 ounces of gold, 24 ounces of platinum. Each necklace requires 6 ounces of gold 3 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 5 ounces of platinum. The store has to use a minimum of two ounces of gold. The demand for bracelet is no less than three. A necklace earns $375 in profit and a bracelet, $225. Formulate a linear programming model for this problem with an appropriate objective function

=number of necklaces to be made

= number of bracelets to be made

Maximize Profit (Z)=

Subject to

Maximum availability of gold

Minimum usage quantity of gold

Maximum availability of platinum

Minimum bracelet required

(Non-negativity constraint)

2. A furniture store makes tables and chairs from plywood and glass. The store has 30 units of plywood, 24 units of glass. Each table requires 7 units of plywood three units of glass, whereas each chair requires three units of plywood and two units of glass. The demand for chairs is between 2 and 4. The ratio between the table and chair is 1 to 2. A table earns $225 in profit and a chair, $145. The store wants to determine the number of tables and chairs to make in order to maximize profit. Formulate a linear programming model for this problems

=number of tables to be made

= number of chairs to be made

Maximize Profit (Z)=

Subject to

Maximum availability of plywood

Maximum availability of glass

Minimum chair required

Maximum chair required

Ratio constraint for table to chair

(Non-negativity constraint)

3. A fertilizer company makes a fertilizer using two chemicals that provide Zinc, phosphate and potassium. A pound of ingredient1 contributes 10 ounces of Zinc and 6 ounces of phosphate and one ounce of potassium while a pound of ingredient2 contributes two ounces of Zinc and 6 ounces of phosphate and 2 ounces of potassium....

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