Question

A company is considering two insurance plans with coverage and premiums shown in the table.​ (For example, this means that​ $50 buys one unit of plan​ A, consisting of​ $10,000 fire and theft insurance and​ $180,000 of liability​ insurance.) Answer parts a and b.		Policy A	Policy B
	​Fire/Theft	​$10,000	​$15,000
	Liability	​$180,000	​$120,000
	Premium	​$50	​$40

a. The company needs at least ​$150,000 fire and theft insurance and at least $2,400,000 liability from these plans. How many units should be purchased from each plan to minimize the cost of the​ premiums? What is the minimum​ premium?

The company should purchase________ units of Policy A and________ units of Policy​ B, for a premium of $________.

b. Suppose the premium for policy A is reduced to​ $25. Now how many units should be purchased from each plan to minimize the cost of the​ premiums? What is the minimum​ premium?

Answer 1

Ltz'units ot poliy A' are Purchascd yunits of poli cy and Psremium . Total subjected to P = 50% + 40y 10000x t15oo o y 1500 00 180,000 x t12o 00 0 y7 2,400,000 ineguality indo guality | Soo o y 120 ooy-24o9000 Chang ing 34 = 30 -150 000 -(2) 3x+ 2y 40 (800 00 X+ Naw 3 2+ 24-4O 2x+3y- 30 2-intorept 40/3 Put Ty= o 2-intercyt Puty-o Z 301 2 c(,0) A (15,0) y-intercapt:- Pat G-interceft:- Put x=o y 20 Golo 3y=30 0, 20) BC0,10) 2by 2' then ubtract Multiply by '3' and (6x+9y) -(6x+ 4y) 90-80 Put in =1o 5y 2x= 30-( 2 2X+ 302) - 30 New Point intasection 7E(12, 2)

po,2) B (o,/0) EC129 2) A15,0) 71 (0,0) DR Leg uired feasible egion with Corner is Ponhon (0, 20), E(12,2) and AC15,0) Shaded Points Cornur Point P= 50 x + 40y Dr0,20) 800 E(12, 2) 680 A ( 15, 0) 750 at EC12, 2) ($6 80) Phemium is minimum Lompamy should punchase 12' units ofpoli cy A and 2' units of policy B9 for minimum Paumiunm of .The 6 80 . (b) If premium bor policy Ais neduced to $25. Then P 25x+ 40y

P = 25x + Corner Point 200 D (o, 20) 380 E( 12, 2) 375 A CIS,O) Premium is minimum $375 at A(IS,D) The Company shauld purchase IS units af Policy A ond nothiry ef PobcyB Minimum Pre mium =$37s