A botanist is interested in the efficacy on predator bugs in reducing pests on garden plants. In particular, two species (A and B) of praying mantis are to be compared to see which devours potato beetles at a higher rate. One hundred grams of potato beetles are released into a cage containing potato foliage, and one praying mantis of each species is introduced into the cage for one week. At the end of the week, the reduction (in grams) of potato beetles is measured. Another identical cage is prepared, but this time, there are two praying mantis of Species A and one of Species B. For the third cage, there are two of Species B and one of Species A, and for the fourth cage of the study, there are two of each species introduced. Let Beta_A be the average grams of potato beetles eaten per week per praying mantis for Species A, and let Beta_B be the average for Species B. Write down a linear model in matrix notation that can be used to estimate Beta_A and Beta_B, giving your design matrix X. Assume that the consumption of each praying mantis is independent of others in the cage. Assume also that there is no natural attrition of potato beetles over a period of one week.