You are considering the decision on the quantity and type of electricity generating capacity to install for meeting the uncertain demand during the next quarter. Once chosen, this capacity remains fixed for the foreseeable future.

Demand over this period is uncertain with a mean weekly demand rate of 1,000,000 units (of electricity) per week and a standard deviation of weekly demand of 200, 000 units. To play it safe you have decided to install sufficient capacity to be able to supply 1,600,000 units of electricity per week. This amount of capacity would indeed cover most reasonable demand scenarios (up to 3 standard deviations above the mean).

The question you are facing concerns the mix of plants that will make up your capacity. You have two types of plant: base load and peak load plants. So the sum of the capacities of your base load and peak load plants should be 1, 600, 000 units of electricity per week. Base plants are more expensive to install, but cheaper to operate. Peak load plants have the opposite characteristic: they are more expensive to operate, but require a smaller capital outlay to bring on line.

The weekly capital cost for a unit of base capacity is 3.3 Euros, that of a unit of peak load capacity is only 2.5 Euros. Capital costs are to be paid regardless of usage. Operating costs are to be paid only as a function of usage. The estimated operating cost for delivering a unit of electricity in a given week with base load is equal to 1.7 Euros, whereas the estimated cost using peak load is equal to 4.0 Euros per unit delivered.

What is, given the above parameters, the optimal mix of peak and base load capacity? (Hint: One additional unit of base load capacity saves you one unit of peak load capacity).