Fast Food Fantasy (Triple-F) cooks different types of hamburgers j = 1,c, 4 in batches.

A batch of burger j consists of at most uj units and requires the entire cooking grill for tj minutes.

Assuming that the hourly demand for each burger is a known quantity dj, Triple-F would like to decide the best batch size for each product. All required batches (and fractions of batches) must fit within the available grill time each hour, and the time required to sell out each burger should be minimized so that none will get too cold waiting to be sold.

(a) Explain why appropriate decision variables for a mathematical programming model of this problem are 1j = 1,c, 42 xj!batch size of burger j

(b) Formulate a system of 4 objective functions, minimizing the time to sell out batches of each burger assuming that demand is smooth over time.

(c) Formulate a single constraint assuring that all batches needed to meet demand each hour can be cooked.

(d) Complete your model with a suitable system of upper-bound and variable-type constraints.

(e) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it single- or multiobjective? Explain.