Formulation of Linear Programming (LP) to maximize Furnco’s profit:

Let x1 be the number of desks produced and x2 be the number of chairs produced.

Objective function:

Maximize z = 40x1+25x2

Considering the constraints,

Constraint 1: Maximum 20 units of wood are available.

Constraint 2: Sell twice as many as chairs as desks.

Expressing the constraint 1 in terms of x1 and x2:

4x1+3x2≤20

Expressing the constraint 2 in terms of x1 and x2:

x1≥2x2

Mathematical model of given LP is,

Maximize z = 40x1+25x2

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Chapter 3.2, Problem 4P

Chapter 3.2, Problem 6P

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At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.

Using Python/PuLP solve At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit. Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250

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Solution Summary: The author explains the formula of linear programming (LP) to maximize Furnco's profit.

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