Problem summary and definitions of quantities

a) Let p, h and q be the number of pizza slices, hot dogs and BBQ sandwiches sold, respectively. The profit, P, is given by

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The last term of 1,100 represents the cost of the booth and the amortized cost of the pizza oven. She has 1500 with which to purchase food for the first game, so . The oven space constrains us as follows, since we can load it twice: . The expected sales are such that . Finally, we require that sales be positive definite quantities: . Using Excel to optimize the profit, P, with these four constraints gives the following solution:

In this scenario, she sells 1,250 each of hot dogs pizza slices, but does not sell any BBQ sandwiches. The profit is 1,150. Given this is above her 1,000 target for net...