It costs$$ $$12$ to make a single unit using regular production and$$ $$15$ to make a single unit using overtime production. Total overtime production is limited to $500$ units for the five month period. The manufacturing plant has a regular production capacity of $250$ units per month and $50$ units in inventory at the start of the planning period. There is a$$ $$5$ per unit charge for holding inventory at the end of each month and a limit of $250$ units ending inventory for any period. What is the total number of units to be produced using overtime throughout the entire planning period if the forecast must be met and costs are to be$$ minimized?

Month

Forecast

January

$250$

February

$200$

March

$300$

April

$400$

May

$500$

Question content area bottom

Part $1$

A$.$

$350$

B$.$

$500$

C$.$

$450$

D$.$

$400$