Suppose the mature height of a plant is a multifactorial trait under the control of five independently assorting genes, designated A, B, C, D, and E, and five environmental factors. There are two alleles of each gene (A₁, A₂, etc.). Each allele with a subscript 1 (i.e., A₁) contributes 5 cm to potential plant height, and each allele with a 2 subscript (i.e., A₂, etc.) contributes 10 cm to potential plant height. In other words, a genotype containing only 1 alleles (A₁A₁B₁B₁C₁C₁D₁D₁E₁E₁) would have a potential height of [(10)(5)]=50 cm, and a genotype with only 2 alleles (A₂A₂B₂B₂C₂C₂D₂D₂E₂E₂) would have a potential height of [(10)(10)]=100 cm. The five environmental factors are (1) amount of water, (2) amount of sunlight, (3) soil drainage, (4) nutrient content of soil, and (5) temperature. Each environmental factor can vary from optimal to poor. If all factors are optimal, assume that full potential height is attained. However, if one or more of the environmental factors is less than optimal, then height is reduced. The state of each environmental factor has an effect on growth. In this exercise, we'll assume that the growth is affected according to the following scale: Environmental Factor State Height Lost Optimal (O)   0 cm Good (G)   4 cm Fair (F)   8 cm Marginal (M) 12 cm Poor (P) 16 cm Thus, for example, if one environmental factor is optimal, two are good, one is fair, and one is marginal, the loss of potential height is . If the loss of height potential is greater than the height potential of the plant, the plant does not survive. If two plants that each have a height potential of 75 cm are crossed, what proportion of the progeny will have a height potential of 80 cm? (Hint: See Figure 19.3e for assistance making this determination.) Genotype Environmental Factor States 1 2 3 4 5 _ a. A₁A₂B₁B₂C₂ C₂D₁D₂E₁E₂ G F O G M b. A₁A₂B₁B₂C₂ C₂D₁D₂E₁E₂ F M G G F c. A₁A₁B₁B₂C₁ C₂D₁D₂E₁E₂ O G G G G