Gone Pro is considering whether or not to produce three new cameras and, if so, how many of each. Each product needs to go through three production stages: machining, assembly, and testing. The table below shows how much time each product spends in each manufacturing stage and the total time available that they have contracted for each stage. The table also indicates, for each product, the profit per unit sold and the one-time setup cost needed to produce them. Camera Models Production Stage HeroSilver HeroGold Fusion Machining 2 3 6 Assembly 6 5 $48 $1000 Testing Profit Setup cost 3 6 $55 $800 4 2 $50 $900 Available 600 300 400 Write and solve a linear optimization model to help Gone Pro decide which products to produce, and in what quantity, in order to maximize profit. What if, for reasons of scale, it is not worth producing any quantity of the Fusion camera unless they produce at least 40 units of it? How would you modify your original model? What happens to the optimal solution in this case? 1. What is Gone Pro's optimal net profit, i.e. after setup costs are incurred? (in dollars) 2. How many different types of cameras are being produced? 3. How many units of assembly time are being used? 4. How many Fusion cameras are being produced?