Wonder Widgets Inc. has 3 plants producing their De-lux Wonder Widget (DWW). Plant A produces 75% of all DWW, plant B 20%, and plant C the remaining 5%.

6% of Plant A's production is defective, 5% of plant B's production is defective, and

1% of plant C's production is defective.

(a) What percent of the total production of DWW is defective?

(b) If a DWW is defective, what is the probability that it was produced in plant A?

6.6.6 Fish Plant Production Quantfisher Inc. buys fresh fish for processing. Quantfisher has an annual contract with its supplier to buy up to 4600 Tonnes at the following set of incremental prices: First 1000 Tonnes (or any fraction) may be purchased @ $0.80/kg. Next 2000 Tonnes (or any fraction) may be purchased @ $1.00/kg. Next 1600 Tonnes (or any fraction) may be purchased @ $1.20/kg. Quantfisher's fish processing plant can operate on a one, two, or three shift per day basis. (Shift two operates only if shift one operates, and shift three operates only if shift two operates.) For each shift there is a fixed cost which exists if the shift operates, but is nil otherwise, and a variable cost per kilogram of fish processed. The costs and shift capacities are: Fixed Cost Variable Cost Annual Capacity Shift Per Annum Per Kilogram (Tonnes) 1 $500,000 $0.50 1700 2 $300,000 $0.70 1500 3 $100,000 $0.95 1300 If a shift operates at all, then the minimum amount processed is 1000 Tonnes per annum on that shift (i.e. the amount processed on any shift is either 0 or greater than or equal to 1000 Tonnes). Quantfisher can sell processed fish for $1.80 per kg. They wish to know what they should do to maximize their annual profit. (a) Formulate this problem. (b) Solve it using the Excel Solver