Chapter 4 Standard form – All variables are nonnegative – Pivot until all numbers in profit are positive Find pivot element and know how to pivot Standard form maximum – Every constraint ≤ to a positive constraint – Solution is read across BV column across to RHS column Standard form for minimum – All other constraints > to a constant. – Objective function has non negative coefficients. – Solution is read down Slack variable rows down to profit row

For #1-2 Determine if table is in final form, if it is state solution if not state pivot element 1. maximum problem 2. minimum problem P S1S2S1S2 BV P x 1 x 2 s 1 s 2 RHS P S1x2S1x2 1. Not final matrix – pivot 1 in s2/x2 2. final matrix – x1 = 4 x2 = 5 C = 20

3. Is the following matrix in standard form, if not what can be modified to put in standard form Minimize C =6x 1 + 3x 2 Subject to: x 1 +x 2 > 2 2x 1 + 6x 2 > 6 x 1 > 0 x 2 > 0 4. Write the duality problem for the minimum problem 3. Not standard form, multiply equation 1 and 2 by negative 1 4. y 1 + 2y 2 < 6 y 1 + 6y 2 < 3 P = 2y 1 + 6y 2

Finance formulas

Chapter 5 w-up 1.If you put $50 in an account monthly earning 8% interest compounded monthly. How much will she have in 4 years? 2.How long will it take an investment to quadruple if it is invested at 3% compounded monthly? 3.Find the proceeds for a discounted loan of $2500 at 22.8% interest rate for 8 months 4.Determine the monthly payment for a $7000 loan at 7.9%compounded monthly for 5 years. 1. $ years3. $ $141.60