(a) Find the inverse of the matrix

Hence find the exact solution of the simultaneous equations
4x + 3y = 900
5x + 7y = 1750
(b) A food supplier makes two different varieties of smoothie, ‘Exotic’ and ‘Floridian’, which it sells in 2-litre cartons. The main ingredients and the profit made on each carton are as follows:The company has 900 bananas, 400 mangoes and 1750 oranges available and wishes to arrange production to maximise total profit. It can sell all of the smoothies that it produces.
(i) Formulate this as a linear programming problem.
(ii) Sketch the feasible region.
(iii) Write down the exact coordinates of the corners of the feasible region.
(iv) Find the optimising production levels of each type of smoothie.

Transcribed Image Text:

4 3 Banana Mango Orange Profit Exotic 4 2 5 $4.50 Floridian 3 $4.00 3.