Chapter 3.10, Problem 3P

Explanation of Solution

Cost minimization:

• Assume “${\text{C}}_{\text{m}}$” be the cheesecakes baked during the month “m”, “${\mathrm{B}}_m$” be the black forest cakes baked during the month “m”, “${\text{I}}_{\text{m}}$” be the count of cheesecakes in inventory at the end of the month “m”, and “${\text{I}}_{\text{m}}\text{'}$” be the count of black forest cakes in inventory at the end of the month “m”.
• The cost minimization “mincost” is formulated as follows,

${\text{mincost=3C}}_{\text{1}}\text{+3}{\text{.4C}}_{\text{2}}\text{+3}{\text{.8C}}_{\text{3}}\text{+2}{\text{.5B}}_{\text{1}}\text{+2}{\text{.8B}}_{\text{2}}\text{+3}{\text{.4B}}_{\text{3}}\text{+0}{\text{.5(I}}_{\text{1}}{\text{+I}}_{\text{2}}{\text{+I}}_{\text{3}}\text{)+0}{\text{.4(I}}_{\text{1}}{\text{'+I}}_{\text{2}}{\text{'+I}}_{\text{3}}\text{')}$

such that,

• All variables >= “0”.
• “${\text{I}}_{\text{1}}{\text{=C}}_{\text{1}}-40$” that denotes the number of cheesecakes in inventory at the end of month “1”.
• “${\text{I}}_2{\text{=I}}_1{\text{+C}}_2-30$” that denotes the number of cheesecakes in inventory at the end of month “2”