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# Mathematics - Linear Operators

Formulate the LP model for the problems below in EXCEL using problem solver:

1. The Big Bang explosives company produces customized blasting compounds for use in the mining industry. The four ingredients for these explosives are agents A, B, C and D. Big Bang just received an order for 2000 pounds of explosive. Agents A and C each costs \$5 per pound, agent B costs \$6 per pound, and agent D costs \$3 per pound. The customer's mixture must contain at least 20% agent A, at least 30% agent B, and at least 15% each for agents C and D. Additionally, the customer insists that there must be at least twice as much agent B as agent C in the mix and that the poundage of agent A must be at least 40% of what's used for agent D. Finally, at least 200 pounds of each agent should be present in the finished product. The company wants to provide the least expensive mixture which will satisfy the customer's requirements.

2. A group of investors has \$500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. Furthermore, they wish to invest the entire amount. The profit after one year, the cost and the number of units available are shown below:

Investment Profit per unit Cost per unit Number Available
(\$1,000) (\$1,000)
Condos 6 50 10
Apartments 12 90 5
Houses 9 100 7
Formulate the model for this problem.

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

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