Question

(1 point) A company is considering two insurance plans with the following types of coverage and promiums: Plan A Plan B Fire/Theft $21000 $31000 Liabilty $159000 $145000 Monthly Premium $75 $68 Premiums are sold in units. For example, one can buy one unit of plan A insurance for $75.00 per month and receive $21,000.00 in Theft/Fire Insurance Two units of plan A Insurance cost $150.00 per month and give $42,000.00 in Thef Fire Insurance. The company wants at least $583.000,00 in coverage for TheftFire Insurance and $3.517,000.00 in coverage for liability insurance How many units of each plan should be purchased to meet the needs of the company while minimizing cost? The company should purchase units of plan A and units of plan B Note: your answer is a dollar amount and should include a dolar What is the minimum monthly premium for the company? symbol).

Answer 1

Let the company y Then should purchase a units of plan A and units of plan B, the problem becomes Minimize cost c = 75x + 68 y Subject to the constraints, (Fine / theft) 21000 x + 31000y z 583000 Ź 21x + 317 > 583 159000 m +145000 y ? 3517000 (Liability) 2 e and and so → 159 x + 145 y = 3517 are integerso x, y zo. also We solve the probleem graphically We draw the constraints o and 2

À (0,2-4.255) B.(13,10) (27. 762,9). 1598 + 1454 23517 21x+31 y 2 583 We get unbounded feasible region with three extreme points BC13,10)., A (0,24.255), C (27.762,0) с Now, we calculate cost at these three points. C =15 x O+(84 x 24.255) = 164a 34 We see that c is CB = (75X13) +(68 x 10) = 1655 cc =(75% 27,762) + (68x0) = 2082.15 minimum at A (0,24.255) but this is an integer programming problem y are are both integers. abs x and

1 if q=0, y = 24, Then constraint does not Satis fies. x=0, y =25, then both the constraints and ® satisfies but costc=1700, then coste will not be minimum ap CB = 1855 if so, B(13,10) will be optimal point. Thus the optimal solution is 12 =15, y =10 min minimun minimum cost should purchase and & 1655 13 so, the company units of plan A and units of plan B. the minimum monthly premium for the 10 company is $ 1655