Math 141
Practice 2
1. Find the point of intersection of the lines whose equations are 4x + 2y = 12 and 3x + 9y =39. A) (5,-4) B) (10, 1)
C) (1,4)
D) (2,2)
2. Graph the constraint inequalities for a linear programming problem shown below. Which feasible region shown is correct?
2 x + 3y::5 12
x~ O,y~ 0
8.
",4)
~ .,0)
b.
",0)
Co
,,~
d.
12,D)
,.~
,,')1
;~
C3,D)
3. Write the constraint inequalities for this situation: Kim and Lynn produce pottery vases and bowls. A vase requires 35 oz. of clay and 5 oz. of glaze. A bowl requires 20 oz. of clay and 10 oz. of glaze. There are 500 oz. of clay available and 200 oz. of glaze available. The profit on one vase is $5 and the profit on one bowl is $4. A) 35x + 5y::5 5, 20 x + 10y::5 4, x ~ O,y ~ 0 B) 35x + 5y::5 500, 20 x + lOy::5 200, x ~ O,y ~ 0
C) 35x + 20y ::5 500, 5 x + lOy::5 200, x ~ 0, y ~ 0
D) 35x + 20y ::5 $5, 5 x + lOy::5 $4, x ~ 0, y ~ 0
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4. The graph of the feasible region for a mixture problem is shown below. Find the point that maximizes the profit function P = 2x + y.
(2,4)
(D,D)
A) B) C) D)
(0,2) (2,4) (4, 1) (3,0)
5. Find an initial solution using the Northwest Comer Rule and compute its total transportation cost. Shop1 Shop 2 Shop 3 2 Bakery 1 1 3 5 4 1 Bakery 2 5 6 rim conditions 3 3 5
6. Suppose you invest in an account that pays 6% interest, compounded quarterly. You would like your investment to grow to $8000 in 14 years. How much would you have to invest in order for this to happen? A) $2125 B) $2290 C) $2650 D) $3475 7. What is the APY for 6% compounded weekly? A) 6.00% B) 6.09% C) 6.18% D) 7.25%
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8. A man cuts back on his latte habit and instead makes $20 deposits each month into a savings account earning 6% interest compounded monthly. He continues these deposits for eight years. How much will the account be worth after eight years? A) $1920 B) $2457 C) $2941 D) $3250 9. A car was purchased in 1985 for $15,000. Its value in current dollars depreciates steadily at a rate of 13% per year. What will the car's value be at the beginning of 2003? A) $1187.25 B) $1223.03 C) $1314.58 D) $1551.05 10. John bought a house in 1947 for $19,000 and sold it in 1997. If the 1947 CPI is 22.3 and the 1997 CPI is 160.5, how much would the house be worth in 1997 dollars? A) $115,157 B) $101,086 C) $94,921 D) $25,356 11. Five years after paying $8000 for some shares of a risky stock, you sell the shares for $4500 (at a loss). Compute the annual returrn to the nearest percent. A) -9% B) -11% C) -14% D) -18% 12. A GreatCity municipal bond with face value $100 currently trades at 107.5 points and yields 6.8%. What is the coupon rate? A) 6.8% B) 7.31% C) 7.5% D) 5.1%
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13. Ellie takes out a conventional loan to purchase a car. The interest rate is 7.5% compounded monthly and Ellie has four years to repay the $12,000 she borrowed. What are Ellie's monthly payments? A) $95.46 B) $139.33 C) $169.53 D) $290.15 14. Suppose you are married filing separately with two dependent children, and you had a taxable income of $38,600 in 2006. Assuming you are not entitled to a tax credit for either child, how much income tax did you pay? A) $9,650 B) $15,002.5 C) $6,207.5 D) other amount 15. Pat invested in her employer's stock program in 1981. The annual yie...