Question

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25.

1) If one of BIlly's machines break down, it usually results in about 6 minutes of downtime. When this happens, Billy's profits are reduced by:

a) $35 b) $15 c) $18 d) $25

2) Which of the following statement are correct?

a) All three constraints are binding. b) The constraint for machine time is binding. c) The constraint for labor and cost are binding. d) The constraint for cost is binding.

3) What is the solution method to choose to solve this method by Excel Solver?

a) GRG Nonlinear b) Simplex LP c) Evolutionary d) None of the above are correct

** NO work needed for these problems **

Answer 1

Solution:

1. With downtime of 6 mins as one of the machines breaks down, the machine hours used would be 300 - 6 = 294. The new formulation solving for new optimal solution will result in optimal quantities produced for Astro, Blijf and Curious, such that total revenue reduces by $35.

Thus, the correct option is (A).

2. As the machine hours and labour hours used result in increase in production of each of the goods, which will result in higher revenue, these two should be consumed at maximum to generate a maximum revenue. So, these two constraints will always be binding.

Budget or constraint in the other hand, will be preferred to be reduced, so it is possible that even with lower cost (lower than the budget) the revenue generated is indeed maximum. So, cost constraint might be binding, might not be binding. (For this question, it is non binding on solving using excel solver). Thus, among mentioned equations, as all other except one says cost equation to be binding, the correct option would be the one which doesn't state that.

Thus, the correct option is (B).

3. As the given constraints and objective function (of maximizing revenue or maximizing profit of minimizing cost, as nothing mentioned about it either of the three possible), both are linear in production levels (the parameters to be solved for) of each of the T-shirts, this is a linear programming problem. So, in the excel solver, the method used will be Simplex LP.

Thus, the correct option is (B).