Linear Programming - Model Formulation 1. Apple Inc. has a demand for its Iphone 8 and Iphone & phones in the Philippities for the 4th Quarter of 2017. They have to allot time to manufacture 7,000 units of Iphone 8 and 3,000 units of Iphone 8s on the last week of August. The profit per unit of Iphone 8s is Php10,000 and the profit per unit of Iphone 8 is Php8.000. The hourly capacity of the machine that produces Iphone 8 is 125 units and the hourly capacity of the machine that produces Iphone 8 is 100 units. Apple Inc. would like to maximize their profit with the available 80 hours of machine time for 1 week for both machines, II. JBC Food Corporation will manufacture two variants of Dingdong snack mix, the plain and hot and spicy. Both snack mix will have US grade green peas, corn chips and curls aside from the usual greaseless peanuts and corn bits inside a dingdong pack. For the pilot production, JBC has 100kg of US grade green peas, 20kg of corn chips and 30kg of curls. The mixture of the plain Dingdong snack mix contains at least 20% of the US grade green peas. The mixture of the hot and spicy Dingdong snack mix must contain at least 10% of the US grade green peas and 15% curls. Assume that one kg of the mixed nuts contributes one kg to one pack of dingdong snack mix. Each kg of Plain Dingdong snack mix can be sold for P500 and each kg of Hot and Spicy Dingdong Snack mix can be sold for P450. Formulate an LP that will maximize Revenue of JBC Food Co. for its pilot production III. I-hop bar is open for seven days a week. Every worker works for six consecutive days, and then takes 1 day off repeating this pattern indefinitely. How can we minimize the number of workers that staff the bar? The number of workers needed on a particular day is given in Table below, Table 1: Worker Requirement Day Mon Tues Wed Thurs Fri Sat Sun Number 24 23 25 26 29 28 21 IV. RDB Company produces product X, Y, and Z and can sell these products in unlimited quantities at the following unit prices: X, $20; Y, $75; and Z, 100. Producing a unit of product X requires 1 hour of labor; producing a unit of Y requires 2 hours of labor plus 2 units of X; and producing a unit of Z requires 3 hours of labor plus 1 unit of Y. Any amount of product X that is used to produce Y cannot be sold. Similarly, any amount of product that is used to produce Z cannot be sold. A total of 40 hours of labor are available. Formulate an LP to maximize the company's revenues. V. Honda is planning a promotional campaign intended to bring prospective buyers of new cars to its showrooms. To every prospective buyer who drops by on a given day, Honda will pay P150. Honda wants to advertise its "P150-3-Look" offer to the public but in order to hold down costs, it wants to get as many serious buyers as possible without attracting too many freeloaders. It is considering advertising on 2 TV shows. The cost of a commercial on each show, as well as the estimates of drawing power per commercial in terms of serious buyers and freeloaders, are given in table below. Table 2: ADS TV Show Cost/Ad No. of Serious Buyers No. of Freeloaders American Movie P85,000 900 4,500 Korean Movie P105,000 1250 3,800 There are at most 4 units of American and 4 units of Korean movie advertising available. Honda hopes to keep total costs (advertising plus the P150 gifts) at or below P2,800,000. Profit for each ad is estimated to be P800 and P1000 respectively for American and Korean movies. Formulate the LP model that will draw as many serious buyers as possible. VI. The OIC needs to assign professors to courses being offered for the coming term. As a basis for making the assignment, The OIC reviewed the past two years student evaluation for six professors who had taught the same four subjects in the past. The average rating for each professor in the 4 courses being considered as shown in the table below. Table 3: Course Assignment Course Prof. Statistics Finance OR Marketing 95 70 N 60 80 0 P 75 80 55 Q SO 95 90 70 M 65 90 70 85 75 60 60 80 65 Formulate the LP model that will enable the OIC to determine the assignment of professors to the different courses that maximizes overall rating