Individual Assessment

The Fantastic Burgers restaurant is considering two alternatives to increase profits: either open a drive-through or introduce a vegetarian burger selection (but not both). The costs for both options are as follows:

For each option, the increase in revenues heavily depends on whether Fantastic Burgers' main competitor, Tasty & Cheap, opens up a restaurant across the street. According to the manager of Fantastic Burgers, this happens with a \(60 \%\) chance. The following table details the increase in revenues for either case:

1. Calculate the profits (i.e., revenues minus costs) for each of the two alternatives (drive-through vs. vegetarian selection) and the two cases where (i) the competitor opens a restaurant and (ii) the competitor does not open a restaurant. Construct a payoff table with the two decision alternatives (drivethrough vs. vegetarian selection) as rows and the two competitor actions (opening up a restaurant vs. not opening up a restaurant) as columns. Which of the two alternatives should Fantastic Burgers select in order to maximize their profits under the maximin, maximax, maximum likelihood and expected value criterion?
2. Fantastic Burgers is unsure about the probability with which Tasty & Cheap opens up a restaurant across the street. Determine for which values of this probability Fanastic Burgers should open a drive-through under the expected value criterion!

Hint: Denote the probability with which Tasty & Cheap opens up a restaurant across the street by \(p\) (as opposed to 0.6 in part (a)). Then write down the expected profits of opening up a drive-through, as well as the expected profits of launching a vegetarian selection (both expressions will be function of \(p\) ). For which values of \(p\) is the first quantity larger than the second one?

Group Assessment

HeavyMachines Inc. produces three types of production machinery (A, B and C) in two factories (1 and 2). Each factory can produce any combination of products, subject to the constraints below. The

Due to demand limitations, HeavyMachines wants produce at most 10 units of product A per day, 8 units of product B per day and 7 units of product \(C\) per day. Each sold unit of product A, B and C results in profits of $\$ 7,000, \$ 5,000$ and $\$ 6,000$, respectively.

1. Formulate a linear program that determines the profit-maximising daily production plan. Do not solve the problem!
   Hint: When formulating the problem, use the decision variables A1 and A2 for the production amounts of product \(A\) in plant 1 and 2 , respectively. Use similar variables B1 and B2 as well as C1 and C2 for the other two products. You will then need one constraint per plant (making sure that the available time is not exceeded), as well as one constraint per product (taking care of the demand limitations) and non-negativity constraints.
2. Find a good solution for the problem in part (a) by hand, and justify why the solution is good. Alternatively, solve the linear program using Excel and determine the optimal production plan?

Price: $14.79

Solution: The downloadable solution consists of 6 pages, 879 words and 5 charts.
Deliverable: Word Document