The Following Comprehension and Related Questions are Purely Hypothetical

MiloBurgers, a fast-food restaurant sells two types of products: “Double Cheese Veggy” (DCV) burgers and “Cheese Veggy” (CV) burgers. The DCV uses 0.5Kg of cheese and the CV uses only 0.2kg of cheese. The restaurant starts the day with 200Kg of cheese but may order more at an additional cost of ₹25 per Kg to cover the delivery cost. Any surplus cheese at the end of the day is donated to charity. MiloBurgers sells a DCV for ₹100 and a CV for ₹80. All in all, MiloBurgers does not expect to sell more than 900 items in total during a day and the owner wants to maximizes the profit for the coming day. Assume that whatever combination is made (a solution to the problem) can be sold. Given this information, answer the given subquestions.

The Following Comprehension and Related Subquestions are Purely Hypothetical Milo The Goofball (MTG) is a company that makes footballs for “Recreation (R)” games and “Professional (P)” games. The process of making a football involves the following three stages Stage-1: Cutting and Dyeing

Stage-2: Sewing

Stage-3: Inspection

It is seen that making a R-game football requires 6 minutes in Stage-1, 15 minutes in Stage-2 and 6 minutes in Stage-3. On the other hand, the football for a P-game requires 12 minutes, 9 minutes and 6 minutes in Stages 1,2 and 3 respectively.

For the coming planning period of 4 weeks, MTG has 340 hours available in Stage-1, 480 hours available in Stage-2 and 300 hours available in Stage-3. Moreover, if required, MTG can avail more hours in Stage-1 at an additional cost of Rs. 200 per hour.

Moreover, a R-game football generates a profit of Rs. 500 per piece and a P-game football generates a profit of Rs. 800 per piece. Furthermore, MTG has forecasted that the maximum number of footballs it can sell is 3000. With an objective to maximize the profit, formulate the problem as a Linear Program and answer the given subquestions.

Milo’s Survey Services (MSS) specializes in evaluating the reaction of customers to new products. A client has hired MSS to ascertain customer reaction to a recently launched product (Frying Pan). During meeting with the client, MSS agreed to conduct door-to-door personal interviews to obtain responses from households with children and without children. In addition, MSS agreed to conduct both “Daytime” and “Evening time” interviews. Specifically, the client’s contract called for MSS to conduct 1000 interviews under the following quota guidelines

i. Interview at least 400 households with children

ii. Interview at least 400 households without children

iii. The total number of households interviewed during evening must be at least as great as the number of households interviewed during the day

iv. At least 40% of the interviews for households with children must be conducted during the evening

v. At least 60% of the interviews for households without children must be conducted during evening

Because the interviews for households with children take additional interview time and because evening interviewers are paid more than daytime, the cost varies with type of interview. Based on previous surveys conducted, MSS estimates the interview costs as given in Table-1

MSS wanted to conduct the interviews so that the overall cost for conducting the survey is minimized. Given this information, answer the subquestions.