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Use the following problem statement to answer questions 1-3. A bank wants to invest in five types of loans. To diversify its portfolio and minimize risk, the bank also invests in risk-free securities. The annual rate of return (%) will be 14 for First Home Mortgage Loan, 12 for Second Home Mortgage Loan, 13 for Commercial Loan, 17 for Automobile Loan, 16 for Home Improvement Loan, and 11 for Risk-free Securities. The bank's objective is to maximize the annual rate of return on investments subject to the following policies, restrictions, and regulations: The bank has $50 million to invest. The risk-free securities must contain at least 10 percent of the total funds for investments. The home improvement loans cannot exceed $8,000,000. The investment in the mortgage loans must be at least 60 percent of all the funds invested in loans. The investment in the first mortgage loans must be at least twice as much as the investment in the second mortgage loans. The home improvement loans cannot exceed 40 percent of the funds invested. in the first mortgage loan. The automobile loans and the home improvement loans together may not exceed the commercial loans. The home improvement loan cannot exceed 30 percent of the total funds invested in the home mortgage loans. [Note: X1 = amount invested in the first home mortgage; X2 = amount invested in the second home mortgage; X3 = amount invested in the commercial loans; X4 = amount invested in the automobile loans; X5 = amount invested in the home. improvement; and X6 = amount invested in the risk-free securities.] D [T/F] The objective function for the model is Max Z = 0.14X1 +0.12X2 + 0.13X3 + 0.17X4+ 0.16X5+ 0.11X6. O True O False Question 2 8 pts [T/F] One of the constraints for the model is X5 0.3(X1 + X2). O True O False Question 3 8 pts [T/F] One of the constraints for the model is X1+X2+X3+X4+X5+X6 = 90,000,000. O True False Use the following problem statement to answer questions 4-6. A coffee shop blends coffee on the premises for its customers. It sells the following three basic blends: Special, Dark, and Regular. To produce the blends, the shop must use four different types of coffee: Brazilian, mocha, Colombian, and mild. The shop has the following bland recipe requirements: Special blend: At least 30% Mocha should be included. Dark blend: At least 45% Brazilian should be included. No more than 10% mild should be included. Regular blend: No more than 39% mild should be included. The shop has 110 pounds of Brazilian coffee, 70 pounds of mocha, 80 pounds of Colombian, and 150 pounds of mild coffee available per week. The shop sells the special blend for $4.30 per pound, the dark blend for $7.20 per pound, and the regular blend for $4.10 per pound. Moreover, the cost of Brazilian coffee is $2.00 per pound, the cost of mocha is $2.75 per pound, the cost of Colombian is $2.90 per pound, and the cost of mild is $1.70 per pound. The shop wants to know the amount of each blend it should prepare each week to maximize profit. [Note: Xij = lbs. of coffee i used in blend j per week, where i = 1 (Brazilian), 2 (Mocha), 3 (Colombian), 4 (mild) and products j = s (special), d (dark), r (regular).] [T/F] The objective function for the model is Max Z = 4.30(X1s + X2s + X3s + X4s) +7.20(X1d + X2d + X3d + X4d) + 4.10(X1r + X2r + X3r + X4r) -2.0(X1s + X1d + X1r) - 2.75(X2s + X2d + X2r) - 2.9(X3s + X3d.+ X3r) - 1.7(X4s + X4d + X4r). O True O False Question 5 8 pts [T/F] One of the constraints for the model is X1s + X1d + X1r s 110. O True False Question 6 8 pts [T/F] One of the constraints for the model is X3s 0.4(X1s + X2s + X3s + X4s). O True False