PA 13-7 (Algo) Goop Incorporated needs to order a raw material to make a special ...

Goop Incorporated needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of 200 gallons and a standard deviation of 100 gallons. Goop sells the polymer for $28 per gallon. Goop purchases raw material for $11 per gallon and must spend $6 per gallon to dispose of all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it has made and the rest of the demand is lost. Use Table 13.4.

Note: If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method.

1. How many gallons should Goop purchase to maximize its expected profit? Use Table 13.4.

Note: Enter your answer as a whole number.

2. Suppose Goop purchases 100 gallons of raw material. What is the probability that it will run out of raw material?

Note: Round your answer to 4 decimal places.

3. Suppose Goop purchases 300 gallons of raw material. What are the expected sales (in gallons)? Use Table 13.4 and the round-up rule.

Note: Round your answer to 2 decimal places.

4. Suppose Goop purchases 450 gallons of raw material. How much should it expect to spend on disposal costs (in dollars)? Use Table 13.4 and the round-up rule.

Note: Round your answer to 2 decimal places.

5. Suppose Goop wants to ensure that there is a 94 percent probability that it will be able to satisfy its customers entire demand. How many gallons of the raw material should it purchase? Use Table 13.4 and the round-up rule.

TABLE 13.4

The Distribution , F(Q), and Expected Inventory, I(Q), Functions for the Standard Normal Distribution

Function

z	F(z)	I(z)
-4.0	0.0000	0.0000
-3.9	0.0000	0.0000
-3.8	0.0001	0.0000
-3.7	0.0001	0.0000
-3.6	0.0002	0.0000
-3.5	0.0002	0.0001
-3.4	0.0003	0.0001
-3.3	0.0005	0.0001
-3.2	0.0007	0.0002
-3.1	0.0010	0.0003
-3.0	0.0013	0.0004
-2.9	0.0019	0.0005
-2.8	0.0026	0.0008
-2.7	0.0035	0.0011
-2.6	0.0047	0.0015
-2.5	0.0062	0.0020
-2.4	0.0082	0.0027
-2.3	0.0107	0.0037
-2.2	0.0139	0.0049
-2.1	0.0179	0.0065
-2.0	0.0228	0.0085
-1.9	0.0287	0.0111
-1.8	0.0359	0.0143
-1.7	0.0446	0.0183
-1.6	0.0548	0.0232
-1.5	0.0668	0.0293
-1.4	0.0808	0.0367
-1.3	0.0968	0.0455
-1.2	0.1151	0.0561
-l.1	0.1357	0.0686
-1.0	0.1587	0.0833
-0.9	0.1841	0.1004
-0.8	0.2119	0.1202
-0.7	0.2420	0.1429
-0.6	0.2743	0.1687
-0.5	0.3085	0.1978
-0.4	0.3446	0.2304
-0.3	0.3821	0.2668
-0.2	0.4207	0.3069
-0.1	0.4602	0.3509
0.0	0.5000	0.3989
0.1	0.5398	0.4509
0.2	0.5793	0.5069
0.3	0.6179	0.5668
0.4	0.6554	0.6304
0.5	0.6915	0.6978
0.6	0.7257	0.7687
0.7	0.7580	0.8429
0.8	0.7881	0.9202
0.9	0.8159	1.0004
1.0	0.8413	1.0833
1.1	0.8643	1.1686
1.2	0.8849	1.2561
1.3	0.9032	1.3455
1.4	0.9192	1.4367
1.5	0.9332	1.5293
1.6	0.9452	1.6232
1.7	0.9554	1.7183
1.8	0.9641	1.8143
1.9	0.9713	1.9111
2.0	0.9772	2.0085
2.1	0.9821	2.1065
2.2	0.9861	2.2049
2.3	0.9893	2.3037
2.4	0.9918	2.4027
2.5	0.9938	2.5020
2.6	0.9953	2.6015
2.7	0.9965	2.7011
2.8	0.9974	2.8008
2.9	0.9981	2.9005
3.0	0.9987	3.0004
3.1	0.9990	3.1003
3.2	0.9993	3.2002
3.3	0.9995	3.3001
3.4	0.9997	3.4001
3.5	0.9998	3.5001
3.6	0.9998	3.6000
3.7	0.9999	3.7000
3.8	0.9999	3.8000
3.9	1.0000	3.9000
4.0	1.0000	4.0000