7. (12 marks) A microbrewery is located in a town which has become isolated after a powerful storm. Until the bridge on the highway into town can be repaired, there is a limited supply of hops, yeast, and barley. A linear optimization model has been made in which the variables are the number of litres of light beer, lager and ale to be made until the bridge can be repaired. There are four constraints for the availability of hops, yeast, and barley, and overall production level. The objective function coefficients are the profit margins of the three types of beer. The spreadsheet formulation (with final values) is: C D E F G A B Beer Model OFV X1 X2 $6,037.50 Light Lager Maximize $2.50 litres 875 3 X3 Ale $2.30 4 $2.80 1375 5 0 6 9 7 7 Constraints 8 Hops Available 9 Yeast Available 10 Barley Available 11 Production 8 8 6 8 10 4 1612515 18000 19000 9875 RHS 20,000 18,000 19,000 11,000 6 12 Using the Sensitivity Report (given at the end), answer the following questions (each is indepen- dent of the others): (a) (2 marks) A bakery in the town has some yeast which is not needed in the short term. They are willing to sell up to 1000 units of yeast at a cost of 25 cents per unit. Should the brewery take the deal, and if so, by how much would the profit increase? (b) (2 marks) Up to 300 units of any combination of hops, yeast and barley could be delivered by boat. What should the boat deliver? Ignoring the cost of the boat trip, by how much would the profit increase? (c) (2 marks) Something happens to the production process which causes the cost of making light beer to increase by 35 cents per litre. Is this in the allowable range? If so, what happens to the profit? Business 2400, Spring 2020, Student Number 11 (d) (3 marks) A ferry drops off another 750 units of yeast, but it is discovered that water damage from the storm has destroyed 2000 units of barley. Are these two changes allowable according to the 100% rules? If so, what happens to the profit